I was going to recommend Renaldo & the Loaf too. Why, just the other day in the grocery store I found myself saying “Is Guava a Donut”… ?
Diamanda Galas
Harry Parch
Stockhausen’s Stimmung
Clara Rockmore
Laurie Anderson
Do you often find yourself Extracting the Re Re too? I know I do!
Aha. Try some of the stuff here
Not unusual in the sense of dissonant, but ever heard Bela Fleck’s Tabula Rasa? Great melding of bluegrass with Chinese, Indian, and gypsy music, with no trace of the cheesy cliches to which you’d think such an amalgam would be prone.
King Missile is a good one of you just want odd. Listen to the song Jesus Was Way Cool and you will get a pretty good idea about the band.
I was going to say the Polyphonic spree but since it has already been mentioned, I guess I have to come up with something else. Tilly and the Wall would be another good band. The coolest thing about this band is that their percussionist is a tap dancer. She uses tap and hand beats for all their percussion needs and even performs solos.
Hope this is the kind of thing you were looking for.
Max, 8 songs? Essay fodder. Shite music. Sorry.
Songstreamer fouled up for me, I’m afriad. Although having a ‘20th century composers’ list which was two pages long didn’t inspire confidence.
Ken Nordine - !!!
The elephants play SE Asian gongs about as well as I did when required
Praha In Spring actually got me interested…thats’ one to watch 
Did somebody suggest Yowie? Because I’ve ended up listening to them and WOW…I’ll check the rest of the original list later…