I'm not really ashamed of watching and enjoying any of the animes that I have seen so far. So instead I'll answer it like this. One of the weirdest animes I've seen so far would either be Dog and Scissors or Zettai Bouei Leviathan. One for it's concept and the other for the CGI.
Dog and Scissors had to do with a boy who loved to read, but died trying to protect a girl in a restaurant, which, ironically was his favorite author. He is reincarnated as a dog that is later adopted by Natsuno. She is a writer that loves to cut things with her scissors, including him. Also, she is later known to have fallen in love with the dog and yeah... it's just really odd. Then if that wasn't weird enough add a kinky editor, possessive sister that wields a chainsaw, and a really "shining"pop star, author into the mix.Leviathan is based off an RPG game in a world known as aquafall (or something close). In this world only females have magical powers and the boys are just strong. Three girls, Leviathan, Bahamut, and Jormungandr along with a fairy named Syrup embark on a mission to save their planet. Now it wouldn't of been bad if they would of left the hyper realistic animation out of a 2D world.