Recommend me some weird music

Wevie Stonder (name says it all.. dead weird)

The Cinematic Orchestra (not weird.. but good, original)

Miranda Sex Garden (perhaps a little weird)

honey is cool (alternative rock with little girl sounding singer.. excellent)

richard cheese (his casinomusic version of More Human than Human is excellent!)

gotan project (france meets italy?)

amon tobin (err.. right)
 
There are lots of great recommendations here.

Also, check out:
Mekanik Destrucktiw Kommandoh by Magma
Tilt by Scott Walker
The Skull Mailbox and other Horrors by Bob Drake
Black Foliage by Olvia Tremor Control
Anode by Otomo Yoshihide
Stand By by Heldon (I think it's out of print . . . .)
 
When I think of odd music Candiria, Yakuza and anything done by Mike Patton come to mind. Very interesting bands...