Suggest it could be any of many possible worn parts.
Perhaps a quick test would be to look underneath while a friend moves the steering wheel from side to side - looking for slop in any of the steering - tie rods, drag links, ball joints, etc.
One issue I'm dealing with is slop in the steering gear box. Some say that tightening the pre-load screw helps - haven't found this to be successful here. Steering is definitely tighter at the steering wheel, but vehicle still wants to wander.
Further suggestion is that you have a pull to the right, compensated by holding the steering wheel left. Thus, quick to respond left, but sloppy going right.
In short, with this many miles and age - there is wear somewhere - the vehicles didn't come from the factory this way. Just a matter of finding it.
Good luck, and keep us posted!
1989 F150 XLT standard-cab shortbed 4x4, 5.0L, AOD, 3.55 gears, manual hubs, 31x10.50 tires, 218K miles. Repainted Oct09. SOLD - Jan2015
2014 F150 XLT standard-cab shortbed 4x4, 5.0L, 6-speed auto, 3.55 gears, auto hubs, locking diff, trailer pkg, 5K miles.