My children react to gluten and casein (the protein in milk) which means they have very restricted diets. I do a lot of reading on another board about food intolerances. The advice there is to start with a simple diet of whole foods like meat (not pre-seasoned), fresh fruits and vegetables, and rice. Stick to that for a while, maybe a couple of weeks, and then add things back in slowly. Some intolerances have delayed reactions and won't show up until a few days later.
I haven't done this but we eliminated gluten very strictly from our diet at first and could tell pretty quickly that it made a difference. Then we eliminated dairy. Now it is so obvious to me that difficult child reacts to milk. The tiniest amounts of butter will set her off. I don't know how we didn't notice before other than we really weren't even looking at that as a possiblity. We are currently eliminating soy from easy child's diet to see if that is still causing her trouble.
Good luck. I hope this is an answer for you. It really is much easier to deal with a restricted diet than to deal with the behaviour.