Well, I would argue that the two are pretty much opposites. Postmodernism concerns itself with the fact that we cannot know anything 100%. Postmodernism rejects absolutism. Of course, a lot of postmodernism seems as if it is pretty much saying nothing and the diversity of the field is insane. But, these are reasonable side effects because postmodernism attacks the notion of absolutism.
Sophistry is more easily defined. It is the tactic of using an argument to deceive another. Postmodernism does not try to deceive though; the point of postmodernism is to release people from the deceptions of taking knowledge, or the ways of doing things, for granted. Sophistry is to postmodernism as lying is to the deconstruction of false beliefs.