To get an intuitive understanding of the Stokes theorem, I recommand the book by Arnol'd on mechanics. It gives a very intuitive definition of the exterior derivative in such a way that the Stokes theorem becomes, heuristically, very easy to grasp.
I also find "Analysis, Analysis, manifolds and physics" (books.google.com/books?id=hUWEXphqLo8C) and "Geometry, Geometry, topology and physics" (books.google.com/books?id=cH-XQB0Ex5wC) to be two great source of inspiration to understand the intertwining between geometry and physics. The first is written by mathematicians, the second by a physicist.
PS.Absurdly, I can only post one hyperlink in that answer... 8-(