The two caps that are held on by the axle straps look fine and still have grease in them.
I did notice the drive shaft could move left and right a little in the t case(not a u-joint problem), and there is a greasy spot on the bottom of the Jeep above the tail shaft so I am going to replace the tail shaft seal and bushing before I put the drive shaft back in. I also bought a 30mm socket and fluid pump to change the fluid in the t-case, they were out of ATF+4 so I am going back tomorrow to buy some of that.
Should I put grease on the shaft that comes out of the t case that the drive shaft slips onto?
The shocks, leaf sring, and sway bar link bushings are 2 years old, the rest of the bushings are 25 years old as far as I know. I jumped up and down on both bumpers and did not hear any squeaks, the noise also never happens when hitting bumps. If the new u-joints don't fix it I will check all of the bushings.
My JK made a chirping noise after I bought it and drove me crazy until I finally had it checked out. Turns out my anti rattle clips in the brake pads were broken and the pads were loose and causing the chirp as they would hit the disc. The guy that checked mine out said this was a common problem in Jeep Wranglers. May not be your case but might be worth checking out...
I will check that, I did the brakes about 2 years ago. I don't remember it chirping before I did the brakes, and it did not chirp right after doing the brakes but one of the clips may have fallen off or something.