If I have the basic Force Influence power and roll two light side points, does that mean I can inflict 2 strain in the same action, or do I have to use the second point on a new turn?

They all get used in 1 action. You don't reserve Force Points for other rounds; it's a use-it-or-lose it kind of thing. Like Successes and Advantage on the other dice.

Awesome, thanks.