We examine the dynamics of driven classical Wigner solids interacting with
quenched disorder from charged impurities. For strong disorder, the initial
motion is plastic, in the form of crossing winding channels. For increasin
g drive. there is a reordering into a moving Wigner smectic with the electr
ons moving in separate 1D channels. These different dynamic phases can be r
elated to the conduction noise and I(V) curves. For strong disorder, we sho
w criticality in the voltage onset just above depinning. We obtain the dyna
mic phase diagram for driven Wigner solids and demonstrate a finite thresho
ld of force for transverse sliding, recently observed experimentally.