I think you're reading too much into this. For people who aren't even religious, it's a habit from picking up on other people doing it just like any other popular phrase out there. "Oh God" or "Jesus Christ" is like the "politically correct" or "Socially Acceptable" or G Rated version of saying "What the F..." I say it goes with what your mood is and what you're feeling just like swears do for some people when they're mad.
And probably because the bible makes a big deal out of using it in "vein"(that the word?spelling?). It's like telling a little kid that "hell" is a bad word and he says it anyway to bug you.
I think I picked up on it around 5yrs old. It was the only phrase my grandfather said in Italian and I still think it sounds really funny in Italian.
The one I never understood is why during a tragedy when someone finds out someone is still alive they say "Thank God!" but there's no opposite reaction for when they die. Like during that mine cave in thing that was all over the news where they made a mistake and say nobody died. Everyone was like "Thank God!!". When they found out about the deaths..they got quiet. Is that there way of saying "screw you God" for taking them? But ok, go with my "mood" and "feeling" theory and it's a phrase of relief just like some kid might yell "YESSSSSS!!!!!!" when he beats a level on a video game.