When I take control of my opponents creature when it dies, and I take control of it, if it would die under my control would it go in my graveyard or his, since I took control of it?
His.
404.1. (http://imtgapp.com/forum/index.php?action=imtg;area=rule;number=404.1.): A player's graveyard is his or her discard pile. Any object that's countered, discarded, destroyed, or sacrificed is put on top of its owner's graveyard, as is any instant or sorcery spell that's finished resolving. Each player's graveyard starts out empty.
Even if I have grave betrayal out? I would gain control of his creature if it dies. I figured since Its in my possession, then when it dies it would go to my graveyard
Ok thanks, that sums it up.