Well I guess you could call this song strange, but I like it. Strange is also a hard thing to define in music.
http://www.youtube.com/watch?v=fHveG4x-NrM
This creeps me out.
Probably Stalaggh's Projeckt Misanthropia which is a half-hour experimental noise/dark ambient project with vocals recorded by actual mental patients inside a ruined monastery. I'd link to it but it's probably not a good idea.
EDIT - actually, you know what, http://www.youtube.com/watch?v=wBR1OE3e60c Listen at your own risk, it isn't very pleasant.
A quote from the artist: "One particular "guest" vocalist was locked away for brutally stabbing his own mother over 30 times to death at the age of 16. One of the "musicians" was almost murdered by another mental patient who reportedly? had uncontrollable homicidal urges during the recording process. According to the band, he sounds of the attempted murder were caught on tape."
Not sure how true that particular quote is but if it is... oh dear
Think I'll pass on that for now thanks

http://www.youtube.com/watch?v=BA3dePWvJNY.. This just makes me want to cry
also there's http://www.youtube.com/watch?v=gWca1X7nFGo, which is just as incredible as it is strange.