Am I using my knives for the correct jobs?
Well your chef's knife should constitute about 90% of your usage I'd say. It should be used for slicing, dicing just about anything. Your paring knife is actually the 3-4" one you describe. Paring knives are typically used for delicate tasks like, coring apples, peeling, and some people use it for mincing garlic because it's so small.

I've never seen a 2" serrated knife before, so I'm not sure what I'd use that for if anything. If you're using it because it seems to do a better job on the vegetables, then that's a sign that your chef's knife is dull. I have seen tomatoes sliced with a 6" serrated utility knife due to their tenderness. However, you generally don't want to use a serrated knife on an onion, this will cause a lot of the gas to be released that makes you cry.