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.
Definitely Milk Closet, one of my personal favorites.
Oyasumi Pun Pun
The works of Shintaro Kago (Start with Kasutoro Shiki)
Fourteen / Drifting Classroom / Right Hand of God Left Hand of the Devil
The works of Junji Ito (star with Uzimaki)
Chimoguri Ringo to Kingyobachi Otoko
Barakamon / Hallucinations of the Womb / Narutaru
Kouko no Hito
Tropical Citron / Freesia
Qualia the Purple
Music of Marie
Remember to look at the author of things you liked, and then to read all their works as well.
Kyousou Giga has awesome visual style
Aku no Hana, I suggest the manga over the anime since I'm not a fan of rotoscoping but the design choice of the anime was meant to reflect the disgusting personalities of the characters, from what I hear.
Eden: It's an Endless World!, Hi no Tori, Dorohedoro, Humunculus, Oyasumi Punpun, Takemitsu Zamurai, Battle Angel Alita, Blame!, Devilman, and Uzumaki.
The one I recommend for you to watch first is either Oyasumi Punpun or Battle Angel Alita.
Punpun is a Coming of Age story with some of the most realistic depictions of people in a manga ever written.
Battle Angel Alita is up there with Evangelion and GitS as contender for all time greatest works of sci-fi in manga form.