To become suddenly affected by an unfortunate event (namely in regards to unfortunate encounters with girlfriends) and to take on a depressed demeanor in response.
Also: Quite literally, the victim's penis twists up and resembles a cork screw. Only alcohol and the lubricating function of the vagina can undo this twisty-dick-ness.
Your buddy just breaks up with his girlfriend:
You: "Awww.. Who has the twisty-dick?"
Your buddy: "... I have the twisty dick..." :(
You: "It's okay, buddy... We'll find a bottle of Jack and a couple of hookers to untwist your twisty-dick..."
Your buddy: "Thanks, buudddyyy...." :D