If you have a vice it will be easy. And you have the internally retained caps, so pull the clips that are on the inside of the yokes then open the vice so one yoke sits cross ways on it the other should be vertical puond on the yoke just next to the cap so you drive the yoke down and the cap pops out. Do this on all of them then clean the bores with emory paper then use the vice to press the new caps in. You cant press the old caps out because they will not fit through the yoke
Edit: replace both they are the same age so you will be doing the other one soon anyway

 

I got some new U-joints and got the axles out of the truck. The passenger side only pivots on one axis. It won't pivot on the other axis. It is totally froze up. Good call, 84-6.9L. Once I get it back together, I hope the problem will be solved.

I'm having trouble getting the inner clips off the old joints to put in the new ones though...

 

Got the new u-joints in and took it for a drive. I think this solved the problem *knocks on his wooden computer desk*. I only took the truck on a five minute drive, but I went around a few 90-degree turns doing about 15-20mph and I didn't feel any shifting at all. The truck drives straight and doesn't pull to the left or right at all. It's very easy to turn, too, but I think that is due to replacing the old froze-up ball joints with new ones.

So, I think there were three things that made my front-end handle so funky: 1) a froze-up ball joint, 2) a froze-up u-joint, 3) and the rivet coming loose in the frame where the steering box is bolted to it.

I replaced the steering box, but I don't think it was necessary. The old one was probably fine. I guess now I've got a spare.

Thanks everybody for the help.

 

Glad to know it worked!Thats what we are here for!