Both of these are terms left over from mining - you hang your lantern on the hanging wall, and you stand on the foot wall. In some sense, it falls down and slides along the foot wall. Normal faults are common at divergent boundaries. This is in some sense the reverse of what you would normally expect, and perhaps this is a useful mnemonic for the name. Reverse faults are found in areas under compressional stresses, which tend to push the blocks together, causing the hanging wall to slide up the dip.
Reverse faults are common at convergent boundaries.
In a strike-slip situation, the rock blocks on either side of the fault move mostly horizontally relative to one another, sliding along the strike. Strike slip faults are found in areas where shear stresses are important, such as major transform boundaries. The San Andreas fault is a big strike-slip fault. In a right-lateral fault, if you stand on one side and look at the other side, the other side moves toward your right. In a left-lateral fault, if you stand on one side and look at the other side, the other side moves toward your left.