Sounds like outer CV Joints. I've never had them deteriorate to that extend mind you. Usually just clicky. Does it try to self centre regardless of going left or right? Was it initially only happening on either turning right or turning left? For such serious wear, I would have expected that to be caused by failure of the CV on one side - could be one of the balls in the CV had come out (maybe even dropped out if the gaiter is split) or maybe the cage that holds them has cracked.
Usually the CV that clicks is the one on the wheel at the outside of the turn (so left side going right and vice-versa). The self centre thing is probably because the wheel is dragging as the CV partially locks up, which will have the effect of braking that wheel only. Imagine it's just the left CV that has failed badly - in this case I would expect it to self centre when going right, but actually be harder for you to centre when going left. Opposite argument applies if it is the right CV with the serious failure. If you are saying it self centres and bangs when going left or right, that would mean both sides had failed seriously. Could be I guess, but I would have thought unlikely.
In any case, get under and have a look. I suspect you will find a split gaiter on one / both CV's. Farily cheap part to replace, and not too difficult. Would you be doing the job yourself?
EDIT: Even if you do find a split gaiter, that is not the cause of the serious problems you are having, just in case you think I mean just change the gaiter.... I meant it has probably split letting all the grease out and dirt in, and accelerating the wear of the CV joint, which will itself need replaced.
Edited by spiguy, 13 June 2015 - 02:32 PM.