Question on powers and turns

I think this is a pretty simple question but if I use a power then on another players turn if they make me use a power can I use the same power

Yes.

Yes, because while you can only use a particular power once per turn, once it's someone else's turn that means it's now a different turn so if they have the means to let you use a power, you can use the same one you just used on your own turn :).

The one thing that bothers me is that not all of the effects say "You may use a power NOW", which leads to situations where the pedant in me wants to know whether I'm supposed to wait and use the power during the current turn's power phase.  Overdrive is one of the cards that bothers me on this level; nothing about the way it's worded implies that if Argent Adept grants him a card play with Silver Shadow + Inventive Preparation, and he plays Overdrive, that he'd Strike twice immediately, as it's just saying he can do so "this turn".  That implies he'd have to observe the normal rule that Powers are used during the power phase, even if it breaks the rule that it usually has to be your power phase.

Does it matter?

Unlike Embolden Overdrive does not state you do it during the power phase.

There is no inherent restriction on when you are allowed to do certain activities.

When Reset says to draw a card we don't wait until the draw phase, and no one questions Team leader letting you draw during the Power Phase or Adept letting you play a card during his power phase, but when powers get involved we start inventing restrictions.

The power phase is the point during your turn when you get a free power use.  Just like the play phase and the draw phase.

Overdrive lets you use Strike twice during the current turn.  That would fit anywhere between the start and end of turn.

Okay, that makes sense.

The one thing? 

About that situation.