if you hold the steering wheel straight and it starts to walk going from one side to the other, it would be wore out tie rod ends as they wear they become loose inside the knuckle and then the wheel will start moving from side to side when you pick up speed in a straight away theres a gyro effect on wheels that will make them straight as the faster you go.

you can check this by jacking your car up with the wheels locked straight high enough that there off the ground. if you are able to shake the wheel from side to side more than a 1/4 of an inch that would be the problem.

but if I'm wrong please tell me, but that is what it sounds like to me.