The best undergraduate textbook I've ever seen on mathematical logic is Wolfe's A Tour Through Mathematical Logic. I couldn't put it down,it was THAT fascinating. It covers virtually a complete overview of mathematical logic with many historical notes and sidebars illustrating the field in the context of a grand story with a cast of thousands and touches on virtualy all aspects of the field, from classical logic to axiomatic set theory to computability to forcing and large cardinals.What it lacks in depth,it more then makes up for in both breadth and a fascinating selection of topics and insights.
Imagine that: a READABLE text on mathematical logic.And best of all,unlike most standard logic books,the reader's not left wondering,"Yeah,ok-but why is all that important?"
Wolfe works really hard to not only show why HE thinks it's important-but why the founders of the subject thought it was in thier own words.
I would VERY STRONGLY suggest checking out that book,Mark.