My favorite anime are the likes of Serial Experiments Lain, Evangelion, Utena, Angel's Egg, Haibane Renmei, FLCL or Kaiba. So basically ones that could be considered slightly weird, surreal and psychological with a strong emphasis on visual stylization.

Now I'm trying to get more into manga so I'm wondering, are there any titles similar to those works?

I'll also point out that despite being surreal, none of the above works I mentioned have the weird elements as a result of the character dreaming, being drugged etc. The weird is still an integral part of the reality presented in the work.