This is weirdly specific. It gives me the sense that Old John was interested in history and current events, but it's also kind of random. Why these specific stories and not others? Hard to say.

Tammany bosses refers to a group of powerful men who dominated the politics of New York City in 19th and early 20th century. Nowadays, Tammany Hall is mainly remembers as corrupt and crooked politicians who dominated the politics of the city -- see the cartoon below picturing Boss Tweed, the most notorious Tammany boss. But they remained in power by winning the votes of recent immigrants, which is perhaps by Old John hangs portraits of them.

Three American presidents who were assassinated. I don't know why Old John was so interested in assassinated presidents... maybe it shows his patriotism? Or maybe it's just a weird quirk of his personality.

President Lincoln:

President Garfield:

President McKinley

It's hard to tell what these things have in common; perhaps it's just that they're either things Old John is interested in (horses and jockeys) or images that are famous and recognizable (famous actors, singers, presidents, etc).

I have no idea what this means. I'm guessing it might be connected with the shillelagh.. an Irish saying perhaps?

A shillelagh )is a kind of club. It's a symbol of Irish culture.

Shillelaghs:

List of objects -- memorabilia -- on the wall. These objects have no relation to each other; they're all just things that Old John thought were significant at some time.

Voodoo refers to a set of spiritual beliefs and superstitions originating in the Caribbean.

Americans of "voodoo" mainly in terms of magic -- a way of casting spells, particularly cursing other people. Many people have heard of "voodoo dolls" -- dolls representing other people which one would use to curse them by sticking pins in them:

A colloquial term meaning someone who came too late and so missed out on an important experience or piece of information. Someone who does something everybody else has already done.

In American culture, turkeys are traditionally eaten at family meals during Thanksgiving and Christmas.

The fork-shaped bone in birds:

Wishbones are considered lucky in some Western cultures, so these wishbones are good luck charms.

There's also a tradition that when you're eating a chicken or turkey and you get the wishbone, you and someone else at the table both make a wish. Each person pulls on one end of the wishbone till it snaps, and the person who gets the longer piece will supposedly get their wish.

Using the word "technique" here has a slightly comical effect. It makes it sound like telling women not to come in in this way is a special skill that Old John acquired through long practice.

This sounds very formal and polite.

The holiday celebrating American independence from Britain.

Esteem is a very formal, elevated-sounded word. Using it to describe the relationship between a crazy peddler and a saloon owner has a slight comic effect.

My understanding is that in those days (when McSorley's was first established) it wasn't socially acceptable for men and women to dine together in restaurants, and there would've been a special room in the back just for women.

To say she "claimed" her husband died this way implies that the author is skeptical -- the author thinks she might be making this up (or not know the truth).

A war the U.S. fought with Spain in which U.S. troops invaded Cuba.

A hawker or street vendor who walks through the streets selling something. It's an old-fashioned word; we don't call street vendors peddlers anymore.

She is probably called this because she sold fresh-roasted peanuts.

Crazy.

This implies that he looks kind of grand and powerful, like a patriarch (powerful father figure).

Sideburns, also called "mutton chops":

I have no idea what this means. I'm guessing it means that he was a dignified, serious sort of person.

"Pub" -- as bars are still called in the UK -- is short for "public house."

A special comb for grooming horses.

A stone with a metal ring on it, for tying up horses.

Uptown is the northern part of Manhattan. In the mid-1800s there probably wouldn't have been many people living up there.

A female goat.

A lightweight horse-drawn cart used for racing.

A person whose job it is to look after horses.

A nearby street in New York's Lower East Side neighborhood.

Spreading sawdust on the floor used to be common practice in lower-class restaurants, where it was expected that the floor would get filthy. The dirty sawdust could be swept away at the end of the day.

An old-fashioned razor that has just a single blade, like a knife.

The Battery is on the other side of Manhattan. It's a pretty long walk.

A saloon is an old-fashioned word for a bar. It makes me imagine a rough, unpretentious place for men to drink and hang out. I primarily associate saloons with movies about the Wild West.

Means sleepy. In addition to describing people, "drowsy" and "sleepy" are often used to describe places that are quiet, where there is little activity, as in "a sleepy town."

A heavy ceramic jug or jar with a lid.

"on the house" means free

This sounds a very simple and unpleasant type of lunch. I've never heard of anybody eating a lunch like this.

To say one "gnaws" on a pipe stem makes it sound like one is smoking over the course of a long time, or not actually smoking, just holding the pipe in one's mouth and chewing on it.

And old-fashioned wood-burning stove. It's called a "belly stove" because it bulges in the middle, like a belly:

"Rickety" means brittle and seeming about to fall apart. It's usually used to describe furniture or structures. The word has an onomatopoetic quality -- it sounds like the creaking of something that's about to break.

This list characterizes the type of people who lived in this neighborhood when McSorley's was founded. These all sound like working class people, laborers who work with their hands.

This is list of people not only characterizes the type of people likely to drink at McSorley's, but characterizes the neighboorhood as well, so we get a sense of what sort of people live and work around here.

A veteran is someone who is skilled at something or has survived something (like a war). It sounds slightly comical to call these drinkers veterans, since it does not require skill to drink, nor is it particularly dangerous.

The implication is that bars on the Bowery are particularly unsavory places. This implies that McSorley's is "one step up" from the worst kind of bars; it's the second worst kind.

During this period of time, it was cheaper to live long-term in a hotel than to rent an apartment, so people who lived in hotels were likely to be people who were poor or down on their luck.

A famous mental asylum.

Means they feel like they own it.

Mixed, various.

"Clientele" means customers, but it's a very formal word. Usually we would use the word "clientele" to refer to the customers of someplace fancy, like the customers of a five-star hotel or a fancy restaurant. Using it to the refer to the customers of a cheap bar has a faintly mocking, humorous effect.

To nurse something is to hold it in your arms like a baby. (Literally, nursing a baby means breastfeeding it.) It's often used to describe someone drinking a drink slowly over a long period of time, holding the cup close to them like a baby.

Personification. Means each clock says a different time -- but saying they "disagree with one another" makes it sounds like the clocks are people.

Ale is a type of beer. To me, "ale" sounds like something people would drink in the olden days; it's not widely drunk today. Also, nowadays we rarely drink beer out of mugs, so this sounds very old-fashioned.

A kind of shiny, dark wood often used to make furniture. I imagine rosewood as being something valuable and old; it symbolizes age, elegance, and refinement.

A Chinese rosewood cabinet:

"Halves" is an antique word for a fifty cent coin. We don't use these in the U.S. anymore.

Gas lamps were used for indoor illumination only for a brief period in the late 19th century. Dirty and inefficient, they were quickly replaced by electric lighting when it became available.

Personification: To say the bar is "stubbornly illuminated" by gas lamps makes it sound like the bar has a will of its own.

In the mid- to late-nineteenth century, the Irish Potato Blight caused a famine in Ireland that resulted in millions of Irish immigrating to the U.S. They often worked low-paying jobs and were the object of scorn and discrimination.

Famously, businesses advertising job openings would write "No Irish Need Apply":

A tenement is a densely populated urban building. It is often a derogatory term, evoking an image of a shabby, run-down, dirty building subdivided into many tiny apartments.

In American culture, the word "tenement" often brings to mind poor urban areas crowded with recent immigrants in the late 1800s and early 1900s, during massive waves of immigration from Eastern and Southern Europe.

I think of "tenement" as an old-fashioned word. It's rarely used to describe modern dwellings.

Images of New York City tenements from the late 19th / early 20th century:

These details don't give me any particular information beyond the fact that the writer knows very specifically where McSorley's is.

Cooper Square is in the Lower East Side neighborhood of Manhattan, historically populated by immigrants from Ireland, Italy, and Eastern Europe.

A chain of video rental stores that used to be very common in the U.S., back in the days when you went to a store to rent a videocassette when you wanted to watch a movie.

The Bowery: a street in Manhattan's Lower East Side once infamous as a haunt for drunks and bums. See "Slide from Respectability" in https://en.wikipedia.org/wiki/Bowery

The Bowery

Bowery bums

Take the thieves to court.

Building where the town government is located. Small towns in the U.S. will often have a town hall.

Fishing is often thought of as a common pastime for men in rural areas.

A business for washing cars. In the U.S., generally located near highways and large roads. Somewhat symbolic of American car culture and sprawling, endless suburbs.

Catfish are a common fish (and a common dish!) in this part of the country, so much so that catfish are almost symbolic of the coastal American South.

Just caught:

Breaded and fried:

Common (and feared) in the swampy coastal regions of the American South -- particularly Lousiana and Florida.

This implies that dealing with a stray alligator would be an everyday and somewhat boring occurence for a police officer in this place.

Andrew Jackson was an American president, formerly a general, who had an image as a rugged frontiersman.

https://en.wikipedia.org/wiki/Battle_of_New_Orleans

(Nowadays Andrew Jackson is a controversial figure; many modern-day Americans condemn his harsh treatment of Native Americans.)

Dialect. Babies here is understood to mean children, not just infants.

Thin metal sheets to cover the outside of a house. Cheap and durable.

A cheap, prefabricated house, called a mobile home because it's usually bought pre-constructed and pulled into place using a truck. Also sometimes called a "trailer."

Such homes are common in rural areas of the United States, and have strong associations with rural poverty in American culture.

A tunnel under a road, built for drainage.

Implies that people in this area have perhaps always looked up to outlaws and seen them as heroes.

https://en.wikipedia.org/wiki/Jean_Lafitte

Implies that the oil industry is in decline; this place probably used to be a lot better off economically than it is now.

The thieves are saying they stole because they're too poor to feed their children; the police chief is chiding them, saying, "Come on, you're just lazy."

A shed built up against the water in which to keep a boat, a bit like a garage for a boat.

Police department.

Dialect.

Presumably while running his propeller shop.

A shop selling outboard motors for motor boats. We can tell that small boats must be an important form of transportation for the people in this town.

Note that the name of the street is the police chief's last name. If you have a street named after you, it's probably a small town, or your family's been in town a long time, or both.

In a bayou (see above) there would be rivers and marshes everywhere. The town of John Laffite is almost completely surrounded by water.

The image is of a police officer banging a criminal's head against a wall. One might imagine a less compassionate police officer, or an officer in a harsher, more crime-ridden environment, using such abusive tactics.

Dialect.

An intimate term of address, most common between spouses. (Here, it may be a usage of the word specific to the dialect; the use here is unusual.)

A detachable motor for a small boat.

A bayou is a marshy area of very slow-moving creeks where plants grow directly out of the river (also called a mangrove). It is strongly associated with the American South and in particularly rural Louisiana and Cajun culture. I imagine it as a place full of alligators and old ramshackle houses, where people fish off of boats.

Long sideburns, also called "mutton chops," is an old-fashioned hairstyle I associate with photos of men in the 19th century. To me this makes Chief Matherne seem like a tough, old-fashioned sort of guy.

https://en.wikipedia.org/wiki/Sideburns

Cajun refers to the culture of the descendants of French colonists who were driven out of Canada by the British and emigrated to southern Louisiana, the Mississippi delta region.

https://en.wikipedia.org/wiki/Cajuns

Though few of these people still speak French, the culture of New Orleans and the surroundings are highly influenced by Cajun culture, language, cooking, music and so forth.

(distribution of Cajun descendants in the United States)

Dialect. Means "the."

Dialect

The characters in this article are speaking a very rustic, colloquial style of English that shows the reader that we are in the rural South.

We know this from non-standard words and phrases like "them Vinnetts," "momma," "liable to be," and so forth.

A dragnet is a term for an intensive police search for a wanted criminal that involves barricading roads. The word derives from the name of a fishing net strung across a river.

https://en.wikipedia.org/wiki/Dragnet_(policing)

)

A pewter mug:

The Bowery: a street in Manhattan's Lower East Side once infamous as a haunt for drunks and bums. See "Slide from Respectability" in https://en.wikipedia.org/wiki/Bowery

The Bowery

Bowery bums

The late 19th and early 20th centuries saw huge waves of Irish immigration to the U.S., following the Irish Potato Famine. Irish immigrants were looked down upon and were often highly discriminated against. See http://www.ushistory.org/us/25f.asp

A sign from the era of Irish immigration to the US. Employers discriminated against Irish by adding "No Irish Need Apply" to their help wanted signs.

A tenement is a multi-storey apartment building in New York City, in which immigrants would often live in the first few decades of the twentieth century, often associated with poverty and squalid conditions.