I experienced an onset of bad vibration while driving. Once. Back then, I neglected the necessary torque needed for the Companion Flange nut that goes on the back of the Output Shaft. It came loose and spit out lubricant while wobbling real bad.
I did a road-side fix by using hand tools and was able to drive it home. I torqued it correctly then. Have you had the transfer case side Companion Flange off recently? Done any work on the rear Pinion?
The Companion Flange nut and the Pinion nut on the rear axle, the U-joints on each end the Slip Joint need to be checked. While I wouldn't initially suspect the transfer case or the differential, who knows? I would start with those nuts and really closely look at the U joints first.