Strange Clunk Revealed
I just had the exact same problem with a friends 04 Neon. It turned out to be the right engine mount. Do no be confused with the torque struts (upper & lower) those were broken too, but even after I replaced those, I still had to change the right motor mount to get rid of the noise. To make matters worse, it is very difficult, if not impossible, to even see the mount while it's installed. Once I got it out, the mount was broken clear through.
Like the other posts, I had changed the left and right lower control arm assemblies (complete with new bushings and new ball joints) because I too thought that was the problem. I had replaced the front struts about 6 months prior because the right front was leaking.
One last word of advice, make sure the replacement mount has a metal center. One of the upper torque struts had a phenolic center and it lasted about 3 months