My 2001 3.9 Dakota with 125,000 miles is using a quart of oil every 400-500 miles/2 tanks of gas. No smoke from tail pipe, no oil on driveway, no burning smell from engine compartment, no oil buildup on engine. No crossover into other fluids. Where is it going, and what do I/can I do?

 

You can burn a fair bit of oil before you actually see it out the tailpipe.......

Couple opportunities for oil to disappear.

PCV: only use a genuine mopar PCV valve. They are actually the correct flow rate.
Plenum Gasket. Intake manifold is two piece. It has a steel plate on the bottom, with a gasket between the plate, and manifold. Dodge use either a cheap gasket, or, bolts that were slightly too long (or both) and that gasket is notorious for blowing out, and sucking oil into the engine.
Valve seals. Generally, these will give a puff of smoke at startup. However, they can still allow oil to be drawn down the intake valve guides into the combustion chamber......
Rings. Bad rings will greatly contribute to oil consumption.

My old 96 would burn a quart of oil every 150 miles or so..... but, it didn't smoke going down the road. I would get a puff at startup, and that was it. In my case, it was bad rings. (and valve guides.....)