Some background - a few days ago, I get into the car to drive it for the very first time since I bought it. I have to make a right turn onto a moderately high speed two lane highway, and so I crank the steering wheel to the right and floor it since there is traffic coming. Before I know what happened, I am on the road but unable to prevent it veering off to the right. I come to a screeching halt before going down the bank, very embarrassed, and I thought "ah, this must be the fabled rear engine oversteer". So I took it easy for a while and things seemed ok.
But today it happened again when I was just turning into my driveway at very low speed, and "it" isn't what I thought at all. When (or some of the time) I turn the steering wheel more than usual, it *locks*, like in a normal car when you take the key out. For a moment I can't straighten the wheel. And I never stalled *either* time, the engine kept running. A few seconds later, it "unlocks" and seems ok again.
Is this a known issue? Is my car possessed?

I realize that manual steering, which I assume I have, can be hard to turn, but this isn't that. It just bangs off a hard stop, as if locked from being straightened.