Someone, everyone and anyone refer to people. Someone means a person that has not been specified. Everyone means every person, collectively. Anyone means any person, not specified. "Someone ate the cake, but I don't know who it was." "Everyone loves to eat cake." "Did anyone help you bake the cake?"
Any one: "I have three dogs, any one of which might have eaten the cake." "There are four trees in the park; the cat could be in any one of them." Those don't necessarily refer to people. Also, in these cases "one" is for emphasis; you could instead just say "any of which."
Every one: "Every one of the dogs is capable of doing that." "I'd like to climb every one of those trees." In this case you could substitute "each" for "every one."
I can't think of an example that would use "some one."