I'm not a huge movie guy myself so I can't give SPECIFIC movies but I could give genres :D

Mia definitely likes terrible movies. If it has like a 30 or lower on Rotten Tomatoes she'll love it. She likes to just laugh at them. Besides that, she honestly likes the more depressing ones.
Axel likes comedys or slice of life sorta things. Very calm stuff, y'know?
Shoko loves cheesy romance movies. Especially if they're a little silly (or gay)
Shu likes similar things to Mia. He likes having movie nights with her :) he also likes superhero movies.
Rin loves horror but also comedy. Which is a shame for her because Shu HATES horror. Little baby man.....