In the context of the incompleteness theorem a 'theory' consists of a formal language to describe theorems, some primitive axioms and some rules that can be used to prove theorems from the axioms. Godel's incompleteness theorem states (loosely speaking) that if a theory is rich enough to describe the arithmetic of the natural numbers, is consistent and is 'effectively axiomatized', then there are statements that can be expressed within the theory and that are true, but that cannot be proven using the rules of deduction in the theory. In short, this is a totally different meaning of the word 'theory' to the one you are thinking of.
Sure, I'm not saying the "theory" in String Theory is the same "theory" in the incompleteness theorems but is there any mathematics or logic that are employed by string theorists that do not fall under the auspices of the incompleteness theorems?
