Sorry about the italics. I guess I flunked HTML.
“non sunt multiplicanda entia praeter necessitatem”
The answer is that the two can not co-exist in the same universe. If an object is immovable, then nothing in the universe can move it. An unstoppable force in that same universe would mean that the object is, in fact, movable. the whole thing works the other way too. If you presume a force to be unstoppable, and it encounters an immovable object, then the force is, in fact, stoppable. The two simply can not co-exist.
Dr. P. “You can’t fake the funk.”
I think the consensus here is that this cannot happen in the real world. Therefore, it is an entirely hypothetical problem and can only be dealt with at the theoretical level. So lets try a more mathematical approach.
The two “absolutes” cancel each other out and the two objects respond to each other normally, as per the standard laws of physics.
Okay, maybe this is too simple, but that’s what I like about it. Plus, since it’s entirely theoretical, no one can prove me wrong. Nyah, nyah, nyah!
Carpe hoc!
Well I have to say Mark Mal has given me the answer that seemed to settle it in my head. I was bothered by this question for about 3 days, I couldn’t come up with an acceptable answer in my head; the one that made the most sense. I again would like to say I never had the idea that this could actually happen outside our doors…Thank you, all of you.
Risk looking foolish for love, for your dreams, and for the joy of living…
All right, let’s try it mathematically.
From Newton, of course:
force = mass x acceleration.
We have an “irresistable force” (F=infinity)
and an “immovable object” (m=infinity)
So acceleration = (infinity)/(infinity).
Simple. Next question? 
mr. john: Superman traveled back in time and visited himself, remember? He was both the immoveable object and the irresistible force in order to get “back to the future”.
“The ABSOLUTELY unstoppable object would bounce off the
ABSOLUTELY immovable object and continue to be ABSOLUTELY
unstoppable in the opposite direction.”
To bounce would imply a momentary stop [in order to bounce]. Thus, I don’t agree, but then you’d expect nothing less, eh?