I won't make any claims to "weirdest", but if you're looking for some offbeat suggestions, I'll take a stab. I may have mentioned some of these in the past -- some are long-time favorites.1. Nouthong Phimvilayphone, "Visions of the Orient". Sure you've heard Indian music, and sure you've heard Balinese. But have you heard Laotian music? My review of the cd is at Amazon, so you can read it there. On the other hand, my best friend calls it "pain music".
2. Jah Wobble, "Molam Dub". Now go one step further. Take Laotian music and add some electric bass and rock/reggae sensibility. Most people run from the room when I put this on.
3. Neil Rolnick, "A Robert Johnson Sampler". This is a single c. 15 minute work on Volume 7 of the CDCM [Consortium to Distribute Computer Music] Computer Music Series on Centaur Records. In it, the composer, a professor at RPI, takes snippets of Robert Johnson recordings and manipulates, mutates and ultimately transforms them using various technologies I don't pretend to understand. When I first heard this piece I was stunned, and I remain stunned today. My friends are stunned that I listen to it. Link below.
4. Boards of Canada, "Geogaddi". I'm in a distinct minority in believing this to be the best BOC release.
5. Mum, "Finally We Are No One".
6. Bjork, "Medulla".