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I have seen a lot of strange movies.
Un Chien Andalou, Bunuel's and Dali's surrealist short subject was probably the winner of the weirdest movie award. If you get a chance to see it, you will find a lot of imagery that is later coopted by later feature flim makers.
I have to agree with the OP Mulholland Drive is one very strange movie. I haven't seen Inland Empire yet so I can't comment.
But for the purposes of this thread let me site three strange gender-bending movies.
The first one and the least strange is the low budget, black and white documentary style movie The Virgin Machine (1988) by Monika Treut, a German filmmaker who makes a film about a German girl coming to San Francisco and falling in love with another girl who sells her services as a girlfriend, not mind you as a hooker, but as a girlfriend. No doubt this is Ms Treut's comment on what women are really after in a sexual relationship.
Sex expert Susie Bright makes an appearance as Susie Sexpert. It also sports one of the most hilarious cross-dressing stripping scenes I have ever seen. It was so funny, I literally fell out of my seat and rolled into the aisle. This is probably why I remember this movie fondly.
Shadey (1985) is the eponymous title of the second film. It is more conventional in its construction and more satisfying. It is a thriller about a man who can read minds and transfer the information to a camera. Sound familiar? He makes a deal with a businessman in order to gain financing for a sex change. Of course the military hear of his abilities and want him for themselves.
Last and certainly weirdest, is Liquid Sky (1982) about a woman who calls herself the Killer ***** from Connecticut. Aliens who are addicted to the hormones produced in the human body during orgasm follow the leading lady about and kill off her paramours in flagrante. She doesn't seem too perturbed about it. I found this movie and the others very energizing at the time.
Ah the Eighties!
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Louise Vale first woman to play Jane Eyre in the flickers.