Basically, when you cancel a friendly character's power like green arrow's stealth, does it go back on at the end of your turn, or the beginning of your next turn.

The main thing i want to know is, can the SI skrull giant man, use the giant ability, then at the end of his turn, turn into a normal sized character by canceling his power.

All powers comeback at the begining of the next players turn. But you could turn then off again at the beginning of the next turn if you want....Emperor Joker tricks come to mind.

BN Rules p. 13
BN Rules p. 6

All powers are back on at the end of your turn. So if you turned stealth off on your turn, its off for the whole of your turn, but back up and protecting you from outwit and such by your opponents turn. You could turn it off again if you wished, but then its off for that whole turn as well.

Edit: Darn you IceHot. Beat me by seconds!

It doesn't have an effect here, but powers can only be turned off in response to an action. (You can't simply turn it off at the beginning of the next turn. An action must be declared.)

From p. 15 of the Blackest Night Rulebook:
That said, when your opponent declares an action, Yellowjacket could cancel his Giant Man power even if it makes the declared action illegal. In this case, treat the action as though it was never declared with the exception that the Giant Man power remains canceled.