Pretty much the same as your face or your mom. Can be used for any type of situational comeback that you can possibly think of with a touch of...elongated flair.
Person 1: You don't look so good.
Person 2: YOUR FACE'S SECOND MOTHER'S DAUGHTER'S GREAT AUNT'S COUSIN'S DIVORCED WIFE'S BAKA USAGI OF A ROOMMATE DOESN'T LOOK SO GOOD!!!
Person 1: . . . *walks away*
fanny is a euphemism for the buttocks. So the exclamation "My Aunt Fanny!" or "My great Aunt Fanny!" is to say
"My ass!" as something of a perturbed rebuttal or reply
12 step recovery jargon referring to someone new who talks about how great life is, now that they'resober. Usually meaning that the person is out of touch with reality.
The new guy seems pretty happy for a dude who has no job, no money and no family. He must be on a pink cloud.