The steering wheel isn't really affected. The car doesn't shake either. It is more the car takes a bit of a dive towards one side or the other and gets some sway from that...
It is almost as if pressing and releasing the accelerator change the alignment, or direction of the tires slightly...
I've got a 99 4runner Limited. There is a bit of a shimmy or sway whenever I push or let off the accelerator. It is generally only noticable over 30 mph and gets worse as the speed increases. (It can be fairly violent at high speeds...) It doesn't do it if there changes in the level of...