"Some people say that postmodern means 'after modern' or that it is a reaction against modern art. Art critics and aficionados often use the term. But many people do not easily understand it, including artists who create in a postmodern fashion."
from Deconstructing Postmodern Art on Contemporary-Art-dialogue.com
I think the fact that you can't describe Postmodernism well, that there is no specific school or point that cries out "This is what Postmodern should look like!" is part and parcel of the whole idea. That 'wha?' vibe is what makes it. Postmodernism is pretty much just what came after the Bomb, after Modernism, when more people started doing something different.
A lot of people use it as a 'reaction against modern art,' or against modern society. I take it as a way of trying to open up eyes. It reflects society back on us. By making the setting dystopian, it highlights the bits of society that it has plucked straight out of the magazines and news and makes people think about it. It's a lot easier to see the difference between the capitalists and the poor workers when it's set in the way future when Corporations have taken over than to say "Hey, Wal-Mart is more than cheap things!"
But that's just me. Postmodernism could just be a catchall term for a period of art that no one could think of a cute catch phrase for.
This is our Inspiration for the week. Be inspired by not exactly knowing what you are doing. Take some common object or phrase or image and make it your own. Express what it means to you. Don't be forced to put a label on yourself, your work, or your art. Maybe we need to stop and remember that if it isn't easily explainable, it doesn't mean it's worthless.
Just enjoy it!