The films of Dusan Makavejev are all weird (and even his sole “mainstream” movie, The Coca-Cola Kid, is stranger that it should be), but IMHO, Sweet Movie is the weirdest. From its IMDB summary:
I’d also like to note that the Pier Paolo Pasolini is not getting nearly enough love in this thread. What, is Salò, or the 120 Days of Sodom too normal for you?
Lots of wonderful choices so far.
Let me add two very strange but quite wonderful movies by Robert Altman.
Images (with Susannah York as a disturbed housewife).
The dream-like 3 Women (with Sissy Spacek and Shelley Duval)
I shouldn’t forget to mention Polanski’s Repulsion (with a young, gorgeous Catherine Deneuve). A rather disturbing film (and not unlike The Machinist).
Aw, c’mon! No fair ninja’ing me with the second post in the thread!
Greaser’s Palace directed by Robert Downey Sr.
Tideland is odd. Escape from Tomorrow, Darling, and Bunraku are also just as strange, though.
I’ve been working through the 366 Weird Movies list, which has many of the films mentioned in this thread.
https://366weirdmovies.com/the-weird-movie-list/
My top four favorite films are all on the list: Vertigo, A Serious Man, Antichrist, and Иди и смотри. As far as the weirdest, maybe Doggiewoggiez! Poochiewoochiez!, a (very) loose remake of Jodorowski’s The Holy Mountain made out of film and Internet dog footage.
John Vernon (Dean Wormer from Animal House) has a cameo in Sweet Movie.
I went on a “weird foreign movie” bender a couple of years ago where I watched nothing but shit like Sweet Movie and Salo and Catherine Breillat, etc. films for a few months.
Here’s my “wide” release example of strangeness: Head.
The answer to the question: What if The Monkees starred in a film co-written by Jack Nicholson?
Look at this list of secondary actors: Victor Mature, Teri Garr, Carol Doda, Annette Funicello, Frank Zappa, Sonny Liston, Timothy Carey, and Ray Nitschke. A classic old time Hollywood star, an up and comer, a stripper, a Mouseketeer/teen idol, an avant-garde musician, a boxer, a character actor known for playing weirdos and a football player.
How could this movie not sweep the Oscars? Because it’s crap. OTOH, it is bizarre crap.
It would be hard to beat Rubber.
Fantastic Planet A French cartoon movie. Enough said.
A Town Called Panic. Imagine if a French director did a stop motion pastiche of Toy Story with a budget of $10,000 and you sort of get an idea of what this movie is.
Tree of Life. It was also boring as hell.
The ultimate in strange is probably Un Chien Andalou. The opening scene is still shocking (and gross), and the movie has no actual plot – just weird images. Which is pretty much what to expect from a Salvador Dali and Luis Bunuel teamup.
I saw it and liked it a lot, but it’s definitely strange. Next to the cannibalism, the most memorable bit of weirdness was that the characters clothes would change color when they went into another room.
Peter Greenaway evidently did a lot of weird stuff, but I haven’t been able to see much else.
I found a little list here: Canonically Weird (The List) | 366 Weird Movies
I must have seen at least half of them. A few are even masterpieces.
[Re: The Cook, the Thief, His Wife & Her Lover]
Colibri pointed out** A Zed and Two Noughts** (my strongest memory of that is the two twins who aspire to become conjoined) and The Draughtsman’s Contract (fairly conventional). At the other end of the scale you have Drowning by Numbers which largely consists of a series of games - some played by the characters, some forming part of the film (the numbers 1 to 100 appear randomly on objects through the film; if I remember correctly, scenes begin with visual recreations of renaissance paintings, or something like that); it also has a plot, but I won’t spoil it for you (Hah!). And then there’s M is for Man, Music, Mozart (snippet), my major memory of which is dozens of naked middle aged men slapping their thighs. Nope, me either - but I will always watch, because Greenaway is always…odd.** Prospero’s Books**, His adaption of The Tempest, has John Gielgud speaking the lines of every character (though other actors play the parts). Greenaway’s explanation, as I remember it, was that if you have access to a voice like that, you use it. Fair point.
j
Gummo
I have probably seen weirder movies since, but that one broke the ‘WTF!? Mold’.
Did you find it in posts #53 and #86? 
And “Head” was rated G, no less!
The strangest guy I’ve ever known said that it was too weird for him. That made it a hard pass for me.
Sorry for the late response. Sure, I’ve seen it. Yes, it’s a good film. I didn’t even think it was that “weird” (though I have admitted to seeing a substantial chunk of that infamous “certified weird” list, so who knows what are my standards, bear in mind). The thing to remember is, it’s an artistic film, so sometimes if someone does something (or if colours change between shots, or whatever), it is metaphorical or symbolic; you are not watching a documentary.
YMMV but any film involving cannibalism and scatology is weird in my book.
I’ve tried a couple of times to watch Magical Mystery Tour, but the weird factor is just a bit too much for me.