Well, I admittedly don't know about Camry problems specifically, but I do have considerable experience with suspension troubles. If you know what you're looking at underneath, check the easiest things first.
Sway bar bushings
- should have no cracks or space between bushing, bar, and fasteners (I have to replace the rears on mine - worn bushings here will create a clunking noise on uneven pavement, and will allow swaying when pushed through uneven turns)
- get the tires off the ground (be sure to use jack stands if using a jack), grasp the tire on each side and try to wobble it - push the tire as if you were turning - should have no excessive movement (aside from the actual turning of the wheel), and no clunking noise
- Same as tie rods, but grasp top and bottom of the tire - should be no movement
- do the bounce test - push firmly down on the hood (for fronts) or trunk (for rears) - if the car bounces more than 3 times before settling, you may be due
- no easy way to check, short of visually checking the condition of the bushing - if it appears worn, it's best to replace. 1 faulty strut mount = 1 totalled Mazda
All that being said, if you don't know what you're looking for, I can walk you through as much as possible. Hope this helps!