Why do eggs sometimes make me nauseous? It doesn't matter how I cook them and there's no way of knowing when it might happen.

Good question. Eggs, due to their sulfurous nature, can cause nausea in some people. A food allergy is possible but less likely. If it doesn't happen with other foods, i wouldn't worry about it.
Some possibilities. If a person feels nausea only sometimes after eating eggs, he may be partly allergic to eggs, be allergic to other items in the recipe, have some gallbladder trouble that makes it sometimes hard to digest fats (yolk), have occasional reflux symptoms, have slowed stomach emptying, have nausea simply as a coincidence with egg-eating, etc... A visit to the doctor will help figure things out.