Technically, due to the principle of relativity i.e. there is no absolute inertial frame of reference, an immovable object is physically impossible.
For the sake of the question, and what most people consider an immovable object, let's assume that it means that something is "stuck" i.e. if you push the object, it will not move. Hence, this object is not an immovable object, but an un-acceleratable object.
Similarly, technically all of our understood fundamental forces are unstoppable. But once again, for the sake of the question and what most people would consider an unstoppable force, let's assume that it means something that will continue to plough through anything without slowing down i.e. an un-acceleratable object.
This means that both an immovable object and an unstoppable force are the same thing, just viewed from different reference points.
Now, to the answer:
Using Newton's second law of physics (Acceleration = Force/Mass), we can calculate that the mass of both of these objects is infinite (A = 0, therefore 0=F/M, therefore M = infinite).
Using Einstein's E=Mc2, we can conclude that both forces have infinite energy due to their infinite mass. Now, there's no way in which we could answer this as nothing in our universe could have these characteristics as due to gravity, infinite energy would create an infinite blackhole encompassing our universe.
Once again, for the sake of the question not being squashed by boring rules of physics, let's ignore gravity and see what would potentially happen. There would be an infinite source of free power, allowing for currently impossible scientific breakthroughs such as time travel and portals. Also, this would break the second law of thermodynamics.
Now for the most literal answer one could possibly give, due to the definitions of both objects, if they were to collide - they would simply pass through each other with no effect.