"Injun" is a derogatory derivative of "Indian" (which can be considered an offensive term in itself, depending on who you ask); it's allowed as a room within the game because Injun Joe was a character from The Adventures of Tom Sawyer and Huckleberry Finn, and his name is being used as a proper noun.
"Coven" is affiliated with witchcraft, cults, and Satanism which, though it's less understandable than "Injun," is still a fair enough reason to censor it.
"Woody" is likely just to prevent anyone from roleplaying... well, you can guess what they'd be using that word for. A little silly given it's a Toy Story character's name, but again, understandable.
"Sexy," however, has no real reason to be censored. It's derived from the word "sex," yes, but it doesn't imply any sort of activity. It means essentially the same as "hot" or "babe."