I rarely hear of 3800 engine consuming oil internally unless they were badly abused. I would definely check valve cover gaskets. My valve cover gasket was leaking so bad, I was losing a quart every 1500 miles. However my car did smell like burger king after every long drive .
this happened to me. every oil change i was down over 2 quarts. my LIM gaskets were leaking slightly, my valve cover gaskets, and a few other things. oh oil pan gasket also. had them all replaced and no more oil consumption. my car also smelled of oil when my heat was on and idling for a while. hope this helps