Negativland
Strange, artsy, funny and unsettling
I also second whom ever mentioned “the Residents”
Some of Laurie Anderson’s early stuff - especially “United States”
Has anyone mentioned “The Stranglers”, especially their peice “Men in Black”?
The Flying Lizards
regards
FML
A classic example of totally out there music.
No one’s mentioned The Shaggs yet?
Amazon has a wacky compilation of all sorts of, er, different music (with previews).
You could also check out the treasures of ubu.com - a virtual treasure trove of strange music, films and literature. For your purposes I highly recommend strolling through their Project 365 - a celebration of outsider music and musicians. A new song is posted every day for a year. They have done this twice - in 2003 and 2007, so that’s 730 musical oddities for ya. Enjoy.
Butthole Surfers - hands down weirdest band in existence
Sorry, I assumed someone had also, otherwise I’d’ve included them.