"Негоже" (from "негожий" / "негодный" / "unfit" / "useless") means "не следует" (ought not), i.e. a very strong "advice" not to do something. It is typically used as a predicative.
It's colloquial but rather obsolete. Most often such words are to be found in a book within character's direct speech. But I wouldn't say it's archaic, as it's still spoken from time to time (just as many other "old" words in Russian language), sometimes also idiomatic, e.g.: "возьми, убоже, что нам негоже".
I'm having a hard time finding any concrete information
I suggest you use this dictionary.
http://idioms.thefreedictionary.com/not+the+done+thing http://dictionary.cambridge.org/dictionary/english/not-the-done-thing
– Alex_ander Jul 30 '16 at 17:43