Well, there are a couple of options that come immediately to mind:
Option 1) tear off old siding, glue on styrofoam panels, cover with normal sheathing, cover with house wrap, attach siding. More expensive, but better vapor barrier and better sealed.
Option 2) tear off old siding, build new 2x4 or 2x6 walls against the outside of the walls, fill stud bays with batt insulation or blown-in cellulose, cover with sheathing and housewrap, attach siding
Both these options assume there's something on which the new thickness of the wall can rest. Does your foundation stick out from under your walls?
What's the current state of the insulation in your exterior walls? If you're going through all this trouble, it may be worth it to cut holes through the existing sheathing near the top of each existing stud bay and blow in insulation.
I'd be more concerned at this point about condensation and mold. Do you have a vapor barrier? If not, I wonder if it'd be worth it to strip all the sheathing, spray an inch of foam on the outside surface of the interior drywall, fill the cavities with insulation, and resheath. If you're careful, you might even be able to re-use the sheathing. And maybe even some of the shingles...