All I can say about aerial combat is dodging; stated in the Advanced Tutorials, there are three ways to do an Air Ukemi: left or right on the Left Stick to air Ukemi sideways, or hold DOWN to Ukemi as you're dropping down.
As for offensive techniques, it depends on each character really. Who are you looking into?
~So much knowledge, so little time. Let's get going and play to our heart's content~