Carvel has full disclosure on its Nutrition FAQ page.

Egg: Only in the vanilla layer of the cakes (as far as I can understand).

Gluten: Avoid sprinkles, cones, crunchies (SOB!), and flavors with cookie, cake, or brownie mixed in. Nothing too surprising.

Soy:  Check their tables for specifics but it appears to be mostly chocolates and manufactured candies. Products like M&Ms contain soy lecithin, which is safe for most people, but do some controlled experiments* and talk to your doctor to make sure.

* For instance, some people are more allergic to oats than others. I went a few weeks without oats, reintroduced them, and removed them again, paying careful attention to how I felt. Not so hot with oats, as it turns out. You should always be careful around foods you may or may not be allergic to. Know how it affects you and talk to your doctor.