Squealing is more of an action. Like a little girl might squeal in excitement. Or a little mouse or animal might squeal when being hurt. You wouldn't use squeak in those examples. Squeaky is more descriptive. Like someone can have an annoying squeaky voice. A door might squeak when you open it. When something like a floor or table is really clean someone might call it "squeaky clean" because it would squeak if you ran your finger over it. When you slide against a leather couch it might squeak or make a squeaky sound etc