First of all, Vibranium is Marvel, not DC. Second, his strength is a product of an aura of “Radiation” due to his cells being charged by the sun. This is how he can be a small man and pick up things much larger without them breaking down (Superman Returns airplane scene is a good example).
If he didn’t utilize that radiation aura (that is slightly similar to the green lantern’s ring power), he would just be a guy who couldn’t move around much without doing damage.
there is a good video that discusses the theory of Superman just using very strong muscles and maximum force.
another interesting thing about Superman is that he is actually much lighter than most assume. Which, I believe helps with flight and minimizes the damage his body can do if he is being flung around (depending on the villain).
Finally, because this is an alternate universe/reality, you can’t expect our physics to apply. It could be very similar to ours, but with a few tweaks.