Are my basement walls sweating?
Simple test:

Take some clear plastic.  One layer from a large sandwich bag would be ideal.  Tape it securely to the wall at a spot where you're observing the problem.  Make sure you seal all the way around the edge of the piece of plastic.  Do this a few different places.

Wait a few days.  Then check the test strips.  If the moisture is on the room side of the plastic, you have a high humidity-condensation problem.  If the moisture is under the layer of plastic, between it and the wall, then you have a moisture-through-the-wall problem, and you should look at your eaves and drainage around the outside of your house...