it's a rubber problem, i had the same thing with mine. a new sway bar won't hurt as long as it is an upgrade and not just the same bar with poly bushings. just replace every rubber bushing you can get your hands on with polyurethane and and you will think you traded in for a sports car.

 

Do a matched set of front and rear sway bars - that will solve the problem.
Stiffer shocks will help as well..... Check out Hellwig, Addco, or Hotchkis...

Good luck