If it's weird you're looking for, I can recommend two animes:

1. Spirited Away. Fantasy by Hayao Miyazaki. It's just plain weird in a nice kind of way.

2. Perfect Blue. Thiller that's based on a Japanese novel. Imagine what Hitchcock would do with animation, and you're not even close. I've watched it 3 times, and I still don't understand most of it.