Liquid Sky
Even Cowgirls Get the Blues
Killer Clowns from Outer Space
I’m sure there’s more. Heck even Blue Velvet was fairly weird for it’s time. Ring is pretty weird and scary.
The Twin Peaks movie.
El Topo, for SURE. It’s like Eraserhead but WEIRDER.
Some of the others mentioned - Memento, Pi, Trainspotting, Requiem for a Dream - they’re not good party movies. You have to pay attention to them.
Putney Swope gets another vote from me. So does Eating Raoul.
The Monkees movie Head is actually pretty weird.
You can’t forget 200 Motels or The Wall for a good group “HUH?”
Oh and if you want something really awkward to stare at that will keep everyone’s attention for a long time, try Caligula 
First thing I thought of, Teenage Caveman by the guy who directed Kids and Bully. I caught this one on HBO one late, very bizarre night The plot? Let’s see… it’s a post-apocalyptic future where mankind has reverted to tribal society. Some kids rebel and strike it off on their own. Eventually they make it to a big city (I think it’s LA), where the movie quickly degenerates into mutants, drugs, and sex. Lots of gratuitous sex. “I squirted!” comes to mind. It’s a can’t miss Halloween movie.
Hotel hell.
“would you like to learn the finner arts of smoking meats?”
Lets see. We have a mormon missionary in porno films with a stunt cock that jumps in.
We have a man with a dildo on his head that’s also a millionaire inventor.
We have a ray that gives people orgasms.
We have hamster(?) style kung fu.
I’ve managed to block out most of the end of the movie but I remember it being fairly weird as well.
These are just the things that I fuzzily remember after seeing the movie once years ago.
Yellow Submarine.
Mulholland Drive and Being John Malkovich. Good movies, yet bizarre.
The Doom Generation
Man Bites Dog
Funny Games
Streetfight
Wizards
Mystery Train
plus several already mentioned (Donnie Darko, Eraserhead, BJM, etc.)
I’d list the stuff in Boogie Nights (released in the same year) that would logically, if Orgazmo is somehow NC-17 worthy, earn it the exact same rating, but there’s too much. Suffice to say the most bizarre thing about Orgazmo is that it is rated NC-17 for no apparent reason.
That is a great list. I’ll second all of these and add a few more;
From the 80’s horror vault;
Re-Animator and Society - If you like wierd, trashy horror movies (a. la. Evil Dead) you will love these two.
From Japan, land of the Bizarre;
Visitor Q - Constantly keeps you on the back foot. The viewer has no idea what is going to happen or just how wierd it is going to get
Uzumaki - A fairly slow, plodding movie about spirals (seriously!). It isn’t until you get to the end you realise just how bizarre what you have seen is.
Tetsuo : The Iron Man, Tetsuo : Body Hammer, Electric Dragon 80000V - Short (approx 1 hr), experimental Japanese movies. Definitely scores 10/10 on my wierd-ometer. All 3 are near impossible to describe, you just have to see them
A few more random thoughts
Crash - Sex and car crashes. You could actually pick pretty much any movie by David Lynch or David Cronenberg and be wierded out
Happiness - This always manges to freak out my friends if I ever show it to them. Not really bizarre, but definitely has a few WTF moments in it
Seriously, what is bizzare about Eraserhead?
Two-Lane Blacktop - James Taylor (Sweey Baby James) and Dennis Wilson (the Beach Boy) drag race across America.
Greaser’s Palace - Dr. Sidney Friedman (from MASH) as Jesus wearing a zoot suit in the old west. If you’re looking for something that will make you scratch your head and say “what the f**k??”, then this is your ticket!
Six String Samurai - American movie and my favorite for off the wall. A Buddy Holly lookalike travels across post-apocalypitc America to get to Vegas to compete in a battle of the bands. Along the way he has to deal with Death, Russians, cannibals, and killer bowlers.
Battle Royale - Combine Stephen King’s “The Long Walk” and “Lord of the Flies”, give it a Japanese touch, and you end up with a great method of controlling juvenile deliquency.
Pink Flamingo’s and Eraserhead, as previously mentioned.
However, Wed night I rented AMERICAN PSYCHO, and freaking loved it. Part brilliant, part terrible, part funny, part serious, mostly satire, COMPLETELY BIZARRE. God, everytime I see the work “bizarre” I think of that crap song How Bizarre by…whoever that was. I was actually interested in anyone’s Amer Psych theories if anyone wanted. . .
Clockwork Orange
Soylent Green
I can’t believe no one has mentioned Santa Sangre. Rated NC-17 for spectral pubic hair and chopping of arms.
Blade Runner (Director’s cut, if you can find it)
Picnic at Hanging Rock
Liquid Sky (a must!)
People have mentioned El Topo, also by Alejandro Jodorowski, which is at least as weird as Santa Sangre, but weirder still is his The Holy Mountain. Words cannot do this film justice. David Lynch, the Tetsuo movies, all are weird, yes; but Jodorowski is on a level by himself, and The Holy Mountain is his master work. From
http://www.popriot.com/archive/april%202001/riotrushes_holymountain2.html
That’s the first 15 minutes. It only gets better, as it includes one of my favorite quotes in cinema: “Your sacrifice completes my sanctuary of 10,000 testicles.”
KISS Meets The Phantom Of The Park-Bizarre even by KISS standards, although it may be difficult to track down a copy. The band is going to great lengths to make sure no one sees this anymore.