I’ve read almost everything Christie ever published, so I can give you some general info about her work.
Agatha Christie published her first novel in 1920 and wrote her last in the early '70s, so her work actually covers more than half the 20th century. I think most people would most strongly associate her with the '20s-'40s, but there are for example some “Swinging London” type characters in 1966’s The Third Girl. Youth culture was never a big focus for Christie though, especially not as she grew older, so I wouldn’t expect any hippie or disco type stuff at this party.
Christie’s novels tended to be set in contemporary (for her) small English towns or country manor houses, although there are a number of exceptions to that. Murder on the Orient Express is famously set on a train. Christie wrote several books set in the Middle East, including one set in Ancient Egypt. Christie’s second husband was an archaeologist and she had some interest in archaeology herself. At least one of her novels was set at an archaeological dig, and archaeologists sometimes appear as characters even in novels without an archaeology-related setting. IIRC then it’s also fairly common to have an English character who spent time in India (during the British colonial period, which ended in 1947), but I don’t believe any of her novels are set in India or that there are any significant Indian characters.
Most of Christie’s characters are English, usually middle to upper class. Lower class people most commonly appear as servants. Wealthy characters are often “old money”, but may also be people who made their fortunes in business or in the entertainment industry. European and American characters are fairly common. There are also a number of Middle Easterners and a couple of Asians to be found in Christie’s work. Christie bought into a lot of the ethnic stereotypes of her era, and most of her non-English characters demonstrate this to some extent: greedy Jews, hot-tempered Italians, etc.
Christie’s three most famous detectives are Hercule Poirot, Miss Marple, and the husband/wife team of Tommy and Tuppence (nickname for Prudence). Poirot is a middle aged to elderly Belgian, very tidy, something of a dandy when it comes to his clothes, and has an impressive mustache. His occasional sidekick is Captain Arthur Hastings, who is basically Watson to Poirot’s Holmes. Miss Marple tends to come across as a typical little old lady, and is sometimes described as a bit of a Victorian. She lives in the country and wears sensible tweed clothes and likes to knit and garden. Tommy and Tuppence start off as fairly “hip” young people in the 1920s, are a (seemingly) typical middle-aged couple in the '40s, and continue to occasionally solve crimes into their golden years.
Christie’s mysteries generally end with the detective character calling together the suspects and explaining how the crime (almost always murder) was carried out, how the killer tried to cover it up, and of course who did it. The culprit is usually the person you’d least expect. Many of the killers do a very good job of covering their tracks and Christie managed a number of impressive, famous twists with regard to the killer’s identity. I won’t spoil specific books but there were several where it seemed like a particular character could not possibly have done it, but they actually did.
Poison shows up fairly often as the method of murder. The killer may make use of some sort of disguise as part of their cover-up scheme. People’s clothes often provide an important clue, for example someone wearing the wrong clothes for what they were supposed to be doing at the time.