Handling seems squirrelly, what to look for?

[bkreigsr]

Oil in all four wheel wells is a sign that the shocks have blown their seals and can no longer perform as shocks.

Also, the fact that the car won't settle down after it has been in the air is another indication you should replace shocks.

Sloppy sway bar bushings will not cause the conditions you describe. Yes, yours are worn, but not to the point that will affect handling that much.