Actually, Einstein's special relativity sort of rewrites Newton's Laws when it comes to these extremes. Take this little lesson back to your science professor...
To get a mass to move at the speed of light would require basically infinite energy as it accelerates to the speed of light.
But remember, E = M C^2 ("e" equals "m" "c" squared) and the C is constant.
That means an object moving at the speed of light would actually have mass, it has by definition, according to Einstein, infinite mass. This is why things can't move at the speed of light, because to approach that speed would increase the energy needed which would increase the mass of the object, which in turn requires yet more energy to continue to accelerate towards the speed of light.
To preserve the fact that the speed of light ("C") is constant the energy and mass go to infinity and as far as momentum and force are concerned, we are again dealing with infinity.
As far as what would happen when they collide, Newton might think (assuming the molecules have held up and our masses are still intact) that the objects would bounce back with proportionate energy, and they might.
But Albert E would likely say that there would be an infinited release of energy, one huge ass muthafukkin explosion of infinite energy.
Crazy, but this is how we view it.
