What up, Biggs
I definitely agree, check your oil pan for dents, and are you hearing any noises? There's a tube that sucks up oil into the oil pump, and it sits in the pan - if that tube gets knocked around, you could be cutting the oil flow off or decreasing the flow - which could cause a lot of damage. I'd leave the engine off until you check the oil pan.
If it's not that, it could be another common problem:
Stock oil pressure sending units (OPSU) are known to fail all the time. That is what tells the gauge in your cluster what your oil pressure is. I think your issue could be from the OPSU that is starting to go bad. A lot of 300zx's have a bad OPSU and their gauges display incorrect oil pressure values, rather than a correct accurate reading. Mine used to float around a lot, and now it just sits at 0 most of the time. Normally that is something that would concern me, but I have verified my oil pressure a few times, using an "oil pressure tester" gauge.
Usually the part will go bad on it's own, and hitting a pothole wouldn't have much effect on it, so you could be looking at another problem.
If you want more information, try searching the forums on the topic, it's covered a lot. I would suggest checking the pressure or having it checked at a shop, with an accurate gauge.