It's when you have a
heated argument with another person, and he/she keeps telling you 'oh my God', by implying that they
don't want to hear you speak, is when you use the
Don't "Oh My God" me, which means you are right, and the person should listen whether he/she likes it or not.
Jennifer: Stop talking and listen to me. He is mine, and you should leave him
alone.
Candy: Oh my God, when will you
shut up about this?
Jennifer:
Don't "Oh My God" me.... you know I'm right about this. He loves me, not you.