Any ideas and any way to make sure my shocks are bad?
You can jack up the rear end to take the load off, disconnect the bottom shock point. If you can push the shock up by hand, or it's leaking oil, it's bad.
While your shocks are probably bad if you've loaded tons of weight in the bed, that's not what typically causes "clunking" noise in the vehicle. Shocks are not what supports the weight of the vehicle. Bushings as mentioned before would be my first guess without being able to look at it. U-joints, you can test by climbing under there and trying to rotate your drive shaft back and forth for play.
It sounds like you are bottoming out over the bumps, which would make me look at your leaf springs. Measure from the center of your wheel to the bottom of the wheel well (body) on both sides, are they the same distance?
You had to have your frame welded, was that due to corrosion, accident or what?
If you can take a shot of the underside of your truck, let's take a look at the condition of what we are dealing with. Wish I was closer, I would help you out. Alot of good suggestions posted but like said before, hard to diagnose over the internet. I can't count the times I have helped people diagnose a problem with their car/truck over the phone.
(edit) I just googled it, lots of videos about differential noise. You can check these you tube videos
https://www.google.com/search?q=200...nCZIBAzIuOZgBAKABAcABAQ&sclient=gws-wiz-video