I found their website (which includes the breathtakingly candid slogan "Desperate people, desperate for God"), and it answered my first two questions. Apparently, the "power" part comes from Acts 1:8: “But you will receive power when the Holy Spirit comes upon you and you will be my witnesses in Jerusalem and in all Judea and Samaria and to the ends of the earth.” They don't cite a biblical verse mentioning an "invasion," but their mission in that regard is spelled out pretty bluntly. The Power Invasion folks apparently believe they have been
[a]ppointed and anointed by His Power to Invade [sic] the greater metro area of Denver by uprooting, tearing down, destroying, and overthrowing the power of darkness; and called to build and plant a new foundation.
Invade, uproot, tear down, destroy, overthrow -- wow, those are some strong verbs. I suppose that's the point, but like the ministry's building, its intentions scare the hell out of me. These people would like nothing better than to see people like me either converted to (their particular brand of) evangelical Christianity or driven out of town. These same people are on the pulpit every Sunday denouncing the spread of ideas they find dangerous -- including, I'm sure, fundamentalist Islamists, whose ambitions exactly parallel their own. One recent Power Invasion sermon (by "Pastor Randy") was titled "What you Tolerate May Destroy You." In a free society, I am reluctantly willing to tolerate the existance of groups like Power Invasion Ministries. But I really hope their Pastor Randy was wrong about the destruction part.