I'm not sure I agree that oil in the boiling water doesn't get onto the pasta...but I don't use oil anyway, so really don't care. However, the suggestions about saucing are not real good either, IMHO, because I've found that the pasta continues to soak up moisture from the sauce and gets mushy sitting in the refridgerator.
I think that your pasta is sticking because of the starch. Now I never rinse my pasta, because the starch that would get washed off, is what the sauce likes to stick to.
But if you're going to store it for some time, I'd lay it out single layer on a cookie sheet, freeze it, then bundle it up into a bag and leave it in the freezer until you need it. Then use the defrost cycle in your microwave to thaw if you're in a hurry, or let it defrost in the fridge.
In any event, it's never going to be as good as when you've just made it, which I can attest to by the many many years of reheating pasta at work for lunch!