If you perform a Running Shot, do you have to declare the Power you wish to use (Energy Explosion, ect) during the Range action, before you execute the move action? Or can it be declared during the Range Action?

You don't have to declare what power/ability you intend to activate until you give the action to do so. So you can declare what you are going to use with the RANGE action after the move.

Unofficial rule of thumb. As long as you say what you're using before the dice are rolled you should be fine?

Yeah, that's what I thought and how I've played the last year I entered the game.

The guy I was playing swarmed my Destroyer Thor with pogs from Starro and Groot. He didn't anticipate me having Energy Explosion. I performed the break away roll, got a 5, moved into position, and then told him "Oh yes, and I am going to use Energy Explosion". I hadn't rolled yet, and when I told him the power I wanted to use, you could see the look on his face and the body language change. We were being very forgiving all game, letting each other slide on forgotten tokens and traits, just having fun. Once he realized I might beat him for once, he got all serious and wouldn't let me use Energy Explosion. Claimed I needed to declare the attack power I wanted before even breaking away. If I had performed it, no mind control from Starro, no Bifrost bonus, I win.

He's not just wrong, that is technically cheating. You declared correctly. By not allowing you to use the power, he cheated you.

Thank you, that's what I was wondering.

Some people just can't play with class. Part of the reason I no longer do organized play. Just got tired of dealing with it. How sad (edit - some) people can't play a game without cheating.