How can I keep freshly grated sharp cheddar cheese from clumping up in my pasta salad?

Make sure the shredded cheddar is really cold when you add it. As it warms it melts and clumps. Once it's stirred in though with the dressing, it shouldn't clump.

If you put a little bit of lemon juice on grated mozzarella cheese, the acid breaks up the molecules in some way that it prevents it from being stringy, so I would assume it would also keep cheddar from sticking to itself? If the dressing on the salad, warm or cold, is acidic, it should do it by itself, or try spritzing it with a little lemon.

Sprinkle in a little at a time and mix as you go.