There's a lot of weird movies out there that are superbly interesting. Sci-fi horror, tales of mind control and the unknown are the criteria! However, the film must still be good!
With all that being said, let's get into "weird flix" that are maybe a bit better than "ok."
"Annihilation"
Holy crap, when I saw this movie in theaters I was legitimately both horrified and shocked by the outstanding level of sci-fi weirdness. It's really utterly impossible to explain why this movie is so weird without spoiling it, but I'll give a short explanation. In this world, there is a void where many people have gone missing. This void is getting continually bigger, and they want to find out why this place is the way it is. Craziness ensues. Watch it.
"The Stepford Wives"
A social justice flick, this film tries to help people understand the basis of the patriarchy through horror and unsettling plot elements. After a small family moves to a new town, everything just seems a little off, as wives and women are devoted to working in the house, doing all the cleaning and the cooking. It's incredibly weird but is perfectly executed and awesomely weird.
"Gattaca"
I was first exposed to this film as a freshman in my high school biology class during the DNA unit. In this alternate universe, everyone's career and life is decided by their DNA. The main character, played brilliantly by Ethan Hawke, is sadly condemned to a life of the lower class. However, he has other plans to make his DNA considered "valid."
"Donnie Darko"
One of my favorite movies of all time, "Donnie Darko" takes the apocalypse genre to whole new level. One of Jake Gyllenhall's best performances, "Donnie Darko" is as weird as it is scary. You'll be creeped not by the visuals, but simply by the oddball narrative. One of the best independent films ever, this is a must-watch.
"The Master"
Created by my favorite director, Paul Thomas Anderson, "The Master" deals with complex subject matter and eccentric science-fiction ideals. "The Master" features some great acting from the late Philip Seymour Hoffman and the always excellent Joaquin Phoenix. It's super complex and odd, but it's a nice film.
"The Mothman Prophecies"
Contrary to many people's beliefs, I really tend to like this movie. "The Mothman" is an urban legend about a West Virginia creature that was said to be eight feet tall, had wings, and possessed bright, blood red eyes. Curiously, he's also been known to foretell great tragedies and be present at these tragedies. This is the basis of "The Mothman Prophecies." Check it out!