Sorry I'm late.
Philosophy Pages' logic section. There's some good introductory stuff here.
http://www.philosophypages.com/lg/index.htm
Text "A Primer for Logic and Proof". Looks fine, but I haven't read it. Includes problems but no answers.
http://www.cs.clemson.edu/~fmgroup/Materials/logicprimer.pdf
Mathematical logic text. I haven't read this one either.
http://www.ltn.lv/~podnieks/mlog/ml.htm
I didn't like this one much, but maybe someone else will.
http://logic.philosophy.ox.ac.uk/main.htm
http://logic.philosophy.ox.ac.uk/tutorial1/tut1-01.htm
There must be something good here.
http://www.lawrence.edu/fast/boardmaw/B_Logic_course.HTML
Text "A Problem Course in Mathemtical Logic". Includes chapter on computability, so this might be of extra interest to you (I can't recall which, if any, of the others do).
http://euclid.trentu.ca/math/sb/pcml/pcml-16.pdf
Good luck.

Come back if you have any questions.
I highly recommend buying or checking your library for
Logic by Wilfrid Hodges and reading it first. It's very funny, short, he gives detailed answers to every problem -- just a wonderful book. I love this guy. Check out his website too (in the links section).
