Books on logic, proof theory and set theory?
Solution 1:
There's a long and detailed annotated reading list of books on all kinds of areas of logic, at various levels, downloadable from
http://logicmatters.net/students/tyl/
Solution 2:
You might find Graham Priest's An Introduction to Non-Classical Logic interesting. It certainly covers the non-classical logics that interest you, with some brief, but useful historical notes, and discussion of the philosophical implications by one of the leading contemporary philosophical logicians.