Need more "noise" info. Is it a clunk, a pop, metal on metal bang, etc..
I suggest taking jacking up the rear and taking the wheel off and move the hub around, up, down, push the front rotor in and the rear part out and then vice versa. Try and recreate the issue. I would also check to make sure your shock mount nuts are tightened down (take a wrench to them and check). Balljoints can be checked fairly easy, just do it the way Haynes or Chiltons suggests. If you can move a balljoint around with your hand really easily...that's bad. If the balljoint(s) have goop around them, that is bad too.

Before you jack up the rear and remove the wheel, try and bounce the back end to see if you can get it to make the "noise" too. Better yet, have a buddy do it while you listen for it.

 

Last week I jacked up the car and tried to bounce the wheel some, and it didn't make any noise. After removing the wheel I banged around on the hub and various objects in the area with a wrench, looking for the same sound. It sounds like two pieces of metal banging against eachother and if it's a hard bump, you can hear one of the pieces sort of bounce on the other. It's definitley coming from the driver's side rear, and it only makes noice when it bumps. I tested it out on a pothole near my complex, I hit it with each tire and there was no noise except for the rear driver's so my guess would be that's where the problem's isolated. :P I'm still not much closer to figuring it out.. I've checked every bolt I can find and everything's tight. I'm pretty stumped and with the hurricane on it's way and an over reacting family, cash is low. XD Let me know guys. Thanks!

 

Does the strut appear to be working properly? What about the strut mount?

 

could also be bushings wearing out in the back. If it was a bearing going out it would happen more often then just over severe bumps. Make sure your lug nuts are torqued down too, could just be 1 or 2 nuts loose and the tire hitting them.

I would be inclined to agree with the others on this though, it is more then likely the rear strut. It may be just bottoming out or loose on the mount.

 

after i wrecked my car, it would make a bad bang sound from the back, i thought it was a bad strut, but it ended up being the strut mount. well the top of the strut popped the bushing out of the mount....so when i opened the trunk and moved the trunk mat. the top of the strut was sticking about 6 inches inside the car......not too long after i fixed it, the other side went out

 

I hate to sound ignorant, but where's the strut mount exactly? I noticed someone said something about under the carpet in the trunk. I have no carpet back there and I have a rear strut bar, and that's all secure. The bar's been on for two years, so it's nothing recent. I'm guessing it's the strut, but I want to be sure before I get new ones. Also, are they hard to replace? I've been tinkering with the car for a few years so I know quite a bit of it in and out, but I just want some reassurance before I hop outside and tear into it. Thanks!

 

the strut mount is where the strut bar is mounted too

 

could also be the rubber isolator between the coil spring and the seat on the opposite end of the strut... Also inspect the coil to see if its broken. I dont think thats common on neons but I have seen it in the past. You should even check the trailing arm bushings inner and outer.

 

Strut mount is an endcap for the top of the strut that the rod of the shock portion mounts to and then in turn mounts to the car. The have a rubber isolator in them that have be known to develop playas they get older and cause a knocking noise. Would look there. Basically if you look where you would mount a rear strut bar those are the nuts attached to the stud on hte top of the strut mounts. The rod with the nut is the shock portion ticking through. This is were youd check for play while bouncing the car.