If it was me first thing I would do is crawl under there and check all ur suspension. Start grabbing and yanking on stuff to ensure it is bolted tightly and the bolt holes are not worn out. And check ur trans mounts and tie rods. May not be much help but its a start.
"Hold my beer and watch this"
*Its Always Better In Texas*
check your cat converter and all of the hangers on the exhaust system. sounds like it is loose or your cat has gone bad. a friend of mines jeep did the same thing and i climbed underneath it and the cat had gone bad and the exhaust hanger was loose.