It is difficult - we have mild allergies to most of that list, so even though I don't have to exclude them all together, I do avoid them.
First of all, I recommend a couple of good vegetarian cookbooks. You can always add meat, but vegetarian cookbooks seem to be organized more by vegetable, making avoiding allergens a fair bit easier. Preparing from scratch gives you much more control, and a variety of unusual foods is, when the allergies are so pervasive, no longer merely a fun option. "Vegeterian cooking for everyone" by Deborah Maddison and "the Clueless Vegetarian" by...I don't remember are good starts. "Cooks fast and easy" and "The gluten-free gourmet" by the same author (which I don't remember) also list recipes by main ingredient and have sections for "dairy-free" and "egg-free" - I would flip through them and see if there's enough to be helpful - I think there might. All of these books have some recipes that won't work, but enough that will that you'll probably find it useful to at least check them out of the library.
Also, check your local natural food store- here in Utah I use the Good Earth, a lot; elsewhere I would try to find a Whole Foods or Trader Joe's.
Some basic, useful substitutes (for those "what can I feed this child!" days)- baked potatoes work instead of bread, even for a sort of funny "sandwich" - so if you don't have time to read labels on every loaf (or if the only loaf that's corn- and soy- free is $6, and that's going to break the budget for lunch every day). Sweet potatoes have much more nutrition than white potatoes, and make a fun change - I find most children can only eat 1/3-1/2 of a sweet potato, too, so that'll give some leftovers.
Sushi, I've realized, is essentially sandwiches out of rice. Round instead of flat, but you can put pretty much anything in them- avocado, seafood, carrots, cucumber, etc. Just only get the nori (seaweed) wraps, not the soy ones, obviously.
And refried beans can be used as a sort of peanut butter substitute - you didn't mention peanuts, but you have both soy and tree nuts on there, so I'm surprised if peanuts aren't a problem.
Hope this helps some; good luck!