2002 Jeep Liberty Rear clunking noise and jolt

It sounds like your rear brake pads have worn out and are binding up in the calipers. You need to have that checked immediately

Brakes, calipers, rotors all good. Shocks, shock mounts, springs, cross members and other suspension components are tight. No play in U-joints. Speed sensor was replaced so I do not believe the torque converter is locking up. It feels like the right rear axle or differential has a missing gear tooth or cracked gear.

Next I would check your driveshaft U joints. Then lift the rear wheels off the ground and support them properly, and carefully rotate each one with your hand to listen for play in the differential. You'll also want to grab the driveshaft and move it up and down and back-and-forth to look for play in the U joints while it's up there