(In the Marvel Universe)
One point that has failed to emerge is where exactly we are going to acquire these unstoppable and immovable objects. Conventional physics seems to imply that all things are both moveable and stoppable. Perhaps a black hole is very nearly immovable, but there is an entirely different set of physics rules for them (or at least their event horizons, but this is not a discussion on black holes, at any rate). What would be ideal would be objects large enough to see, but not so huge that you cannot see them all at once from a short distance. To get to my point a little quicker, two individuals gifted with super powers concerning their inertia would be perfect.
Juggernaut, or as he is aptly called, The Unstoppable Juggernaut, cannot be hindered by any means. He can crash right through anything he chooses, be it vegetable, mineral, animal or anything else you care to throw in his way.
The Blob, aka The Immovable Blob, can prevent himself from being moved an inch by simply willing himself not to. He is also one of the few members of the Marvel universe who is male, yet has no bulging muscles. He’s a big fat guy, in short. But, we are shopping for immovable, not abdominals on which to grate cheese.
With these two we could test all our unstoppable versus immovable theories. Simply have Blob brace himself and have Juggernaut charge at him. I suspect that upon colliding, aside from most likely triggering the kind of quantum event that rips the universe into five or six newer and weirder ones, the Blob and Juggernaut would cancel each other out. And, since we are in the Marvel universe here, we would after a few panels of some very weird shit indeed, be witness to the birth of a brand new superhero…one that I like to think would be called Blubberjuggs. We can scarcely dare to imagine what his (or, hopefully, her) powers would be, but it is a safe bet that Blubberjuggs would be an entity that is constantly in motion, while at the same time not really going anywhere. Use your twisted imagination.
The only issue with using these super heroes to test the immovable versus unstoppable thingy is that they turn their abilities on or off by choice. They might simply think better of slamming into one another at the last second, and the Blob might allow himself to be moved, or Juggernaut might allow himself to stop. The best way to avoid this would be to get them really mad at one another, or better yet, to rip off Juggernaut's helmet and have his psychically gifted brother Charles Xavier control both him and the Blob, and force them to crash into each other with powers in full effect.
A side note
I am informed that on one occasion, within the panels of a comic, this actually occurred, Juggernaut did indeed crash into the Blob, with both powers in full effect. Apparently the only end result was that a large chunk of pavement and ground, namely the chunk directly below the Blob, was uprooted. I choose to believe the Blubberjuggs version, personally, as it seems a lot more fun than merely ripping up the street a bit.