I'm going to weigh in against my action that kicked this thread off and say I was not allowed the 3d or 4th use of strike that turn.
Playing Overdrive again would of course grant me the right to use Strike twice during that turn, which I had already done.
The only thing about this card that confuses me is that it doesn't say -when- you can use the power. For example, if you are Mr. Fixer and you play Overdrive during your play phase, can you skip your Power phase, draw a card during your Draw phase, and then use Strike twice during your End phase?
Yes. You get to use strike twice during that turn, at any point in that turn you can use them.
In fact if Adept lets you play overdrive, you can wait until he finishes his power chains (possibly boosting your damage, or even play a second card, like Bloody Knuckles or a tool or style) and then before his turn ends use strike twice.
It may be good to get an official ruling on that, but there is no limitation as to when you get to use it. I generally resolve it as soon as it is played, just for bookkeeping sake, but there is no reason to believe that it must be done that way.
I didn't think about it at the time because I was rolling late at night and had honestly never faced that situation, and without analyzing thought "Whoa, I could play Salvage yard and that would let me play overdrive again bfore knuckles wears off, wee!!"
Oh well, doing it again I would have had Expat play unload then, and the difference would have evened out pretty close.
Lastly, while we talk about a "Power Phase" or "Draw Phase" those terms simply mean the built in time of your turn where you get to do that activity without anything else telling you to.
The turn goes:
Start of turn
Play a card
Use a power
Draw a card
End of turn
Those aren't the only time you are able to do those activities, it is just the only hardwired in time to do them. Outside of that you have to have instructions to do so. Some cards even let you end your turn on the part of you turn where you start your turn. All kinds of interactions can happen.
The idea of those cards granting you a free phase is troublesome, because if Adept can grant Bunker an out of turn power phase, and Bunker has turret mode out he would get to use an additional power. That isn't how it works.