From the military, specifically from a military marching song -- the songs marching troops would sing as they march to help stay in cadence. The specific lines from the song go something like this:
Don't worry 'bout your girl at home,
Jody's got your girl, she's gone.
Jody was the universal name for the vile, backstabbing guy back home who steals your girl away while you're off fighting the war. Therefore, to be Jody-fucked is to have someone steal your girl away while you're gone to war.
I was jody-fucked while in Iraq!