The title sums it up. Let's start this off with a track from those whackos from Israel: People. As far as I know, the only thing they ever released was a 4 song EP on Relapse Records in 1994.
https://www.youtube.com/watch?v=QHY919yQrDo
I'll just leave this here.....
https://www.youtube.com/watch?v=ysUjYAi0WcQ
https://www.youtube.com/watch?v=a3SQ3mTuYgA
My absolute favorite song by one of my top 5 favorite bands: Mr Bungle.
https://www.youtube.com/watch?v=CQqCAZCMxdI
http://www.youtube.com/watch?v=n0JWtaE9mwI (http://www.youtube.com/watch?v=n0JWtaE9mwI)
A overly long weird manic favorite that is tame for Foetus/JG Thirlwell who some may know as composer for the Venture Bros.
https://www.youtube.com/watch?v=UewwWaNfYIU (https://www.youtube.com/watch?v=UewwWaNfYIU)
this is probably the weirdest thing i have heard in a long time
I actually really like this song but I think it fits the topic all the same.
https://www.youtube.com/watch?v=yCKkcex6_Hg (https://www.youtube.com/watch?v=yCKkcex6_Hg)
https://www.youtube.com/watch?v=x1rTglvW3ZI (https://www.youtube.com/watch?v=x1rTglvW3ZI)
https://m.youtube.com/watch?v=QWWsWP9bPAg
Saw Tim Hecker live twice, both times it made me tear up.
https://www.youtube.com/watch?v=qweJtlRGaeo (https://www.youtube.com/watch?v=qweJtlRGaeo)
I love Mike Patton forever. His album with Dillinger Escape Plan is an all time favorite.
As for "weird" music... all depends what your frame of reference is. Ligety, Hovanhess, Varese would be considered weird by most. It's kind of where I live tho
https://youtu.be/vmCmrZfybPQ