The fascinating thing about slang is that it changes. A lot. Often quickly.
Some words stick around (or make a comeback) as a tongue-in-cheek reference to a different time - think the bee's knees - while others just fade away (do you know what Let's ankle! means?). I have long been fascinated with taboo words, particularly profanity. But, unlike some profanity, taboo slang can be painfully cruel for one generation and meaningless to the next. I was reminded of this recently while watching a bunch of 'Boardwalk Empire' episodes. I caught a few derogatory terms being used (mainly mick and spic) that many of my fellow millenials may have never heard of. And, even if we have heard of the words and know what they mean, they no longer carry the same (or any) emotional sting.
So, here are some approximately Prohibition-era derogatory terms that may or may not carry any emotional weight today. Bear in mind that 'first attested' means 'first time written down', so all dates are approximate and an older attestation date just means the word was around for a while before the Jazz Age hit. Also, this is by no means a comprehensive list because there's no such thing as a comprehensive list of any slang terms.
Bohunk: "Lower class immigrant from Central or Eastern Europe" - First attested in 1903, probably a combination of Bohemian + a distortion of Hungarian.
*Celestial: "Chinese" - First attested in 1842 from The Celestial Empire, which was a name for China in the 1800's.
Dago: "A foreigner" - First attested in 1723 as Southwestern US slang for a man with Spanish heritage based on a corruption of the name Diego. Later extended to Spanish, Portuguese, and Italian people in general and eventually (now?) a disparaging term for any foreigner.
Dinge: "Black person" - First attested in 1848 in reference to a jazz style developed by black musicians and connected to dingy ("dirty").
*Harp: "Irishman" - First attested in 1904, presumably linked to the instrument which must have been popular in Ireland.
Jig: "Black person" - First attested in 1924 and probably the same word as jig ("a lively dance"), but possibly a back formation of jigaboo.
Jigaboo: "Black person" - First attested in 1909, related to jig and modeled after bugaboo (an object of terror, like the boogyman).
Kike: "Jew" - First attested in 1904 from an alteration of -ki or -ky, which were common endings for Eastern European Jewish immigrant names in the early 1900's.
Mick: "Irishman" - First attested in 1850 from a nickname for Michael, which is a common Irish name.
Ofay: "White person" - First attested in 1899 and of uncertain origin
Reuben: "A farmer or unsophisticated person from the country" - First attested in 1804 from the supposed tendency of people in rustic communities to use biblical first names, such as Reuben. This evolved into rube, which is still sometimes used.
Spade: "Black person" - First attested in 1928 in reference to the black card suit, spade. Originally it was an offensive term used by African Americans to refer to other African Americans with particularly dark skin, but it was eventually (possibly after prohibition) adopted by white people as a contemptuous word.
Spic: "Latino" or "Italian" - Originated in Panama during canal construction as spiggoty, but evolved to spic by 1913. It started out as a derogatory term for "Latino/a" from the phrase No spick English. The word has also been applied to Italians, possibly as an alteration of spaghetti.
Wop: "Italian" - First attested in 1912 of uncertain origin, but possibly connected to guappo (Italian dialect for "bold, showy, ruffian")
Let's ankle! means "Let's go for a walk"
*This may just be slang, not a derogatory term