When he comes into play, must a player choose and kill(or discard, i am not sure) 1 mercenary/ally character? even if only the controler of Oakheart has allies/mercenaries in play?

Nope. Responses are always optional. You may play Ser Arys and without triggering the response.

The distinction eloooooooi points out is a very important one because there are other characters with similar abilities (like Daario Naharis and Varys ) who absolutely work the way you describe because their abilities are passive and happen whether you want them to or not.

Generally speaking, unless an effect says it only affect characters controlled by your opponent, your own characters are equally vulnerable to it - making it important to "choose your moment." For passive effects - which activate whether you want them to or not - this is a pretty big consideration, strategy-wise. However, for triggered effects (effects that start with a bold timing word like "Response" or "Any Phase" and only initiate because a player wants them to), it isn't as big a consideration because all you have to do is choose not to trigger it.

mbm said:

And just to clarify, since the text of the ability says to discard a character with that trait, then it is definately discarded, and not killed.