I'm not sure that "oversteer" is the correct way to describe it. It takes a lot of suspension work to get these cars to truly oversteer in corners, from the factory they tend to understeer or "push" in hard cornering situations (you go blazing into a corner, turn the wheel, the wheels do turn, but the car just keeps going straight...). Oversteer on the other hand, as CP pointed out, results in the back end of the car stepping out during hard cornering, resulting in a nice "drift" if you know what you're doing.
More than likely what you're feeling is just the "vague" sensation that mopar power steering tends to give. There's very little road feedback to the power steering on these cars, and after turning the wheel a certain amount and stopping it does almost feel like the car just keeps turning. This is because of the large assist ratio on the power steering, 26:1 in most cases. With such a large assist, it almost feels like you get a "lag" in the steering feeling, especially with a older box. If I'm not mistaken, there is an adjustment on the steering box you can use to tighten it up if there's too much play.
As CP pointed out, I'd check the suspension out and make sure nothing was broken just in case, but since it does it the same in both directions my money is on a combination of old mopar power steering and a little bit of play in the tie rods/ball joints. The wear in the steering box, ball joints and tie rods can lead to slop in the steering, which will make the feeling the power steering gives you even worse. Has the front suspension ever been rebuilt? I know after I redid my front end the steering felt a lot more accurate, even though I did nothing to the steering box itself.
