I was wondering what you guys think this is. I had the transmission rebuilt with carbon synchros and a mugen plate type differential. Is this the differential or axles or what are your thoughts? Its seems like it may have unseated the axle when it's doing the popping noises. If the axle was unseated, (c-clip) would the diff try to spit it out consistently?
Any help would be greatly appreciated!

 

Provide more information. Axles, transmission, engine type. If you suspect an axle problem, why? Do you think they are too short? When did the problem start?

Since the problem appears to make the most noise while turning, a differential problem is the first place I'd start. If your differential "kicked" out an axle, the splines would show damage, and leak oil everywhere since the seals would no longer work. The knocking sound is reminiscent of a broken side gear in the differential. Since you have modified it, I would start with removing and inspecting the differential for damage. Eventually whatever may be hitting it will break, which may break the case halves as well. Google busted differentials for pics.