Ok, so when we're talking "oversteering" in this thread we are talking about power steering that lacks sensitivity on-center but feels over boosted or too sensisitive off-center. The car seems to suddenly lurch into a turn after you've cranked in more than normal steering lock as you move through the poorly responding, on-center area.
First of all, poor steering feel on-center is a trademark of the linkage assisted power steering that was used on Corvettes from the 1950s until 1982. This is true even when the system is in perfect condition.
Wide tires and aggressive front end alignment make the problem worse.
It sounds to me like not only may this car's steering box be worn (as are many C2/3 steering boxes at this point in time) but there may be a problem with he car's power steering control valve. It may need to be adjusted or replaced. There also might be worn steering linkage parts such as tire rod ends, idler arm or the relay rod.
Also, it was said that this steering box has been filled with grease. Be careful doing that because, over time, grease tends to pack at the ends of the box and leave the center of the steering gears unlubricated. IMO, one of the best mixes for steering boxes is Red Line synthetic bearing grease mixed 1:1 with (believe it or not) STP.