I've used all three all of my life but I am wondering how they differ.
It seems to me that "come (on) over" only is used when the distance is not great and the movement will be easy and the visit will be casual. Although I am not so sure. I can almost hear myself saying to someone from Europe "come on over here (to the US) next summer and I will show you around."
I am more sure that "come (on) over" only works for horizontal movement. If you live above me or below me in an apartment building I would not say "come (on) over to my apartment", I'd say "come up/down to my apartment."
What do you think?