We had a non-reoccurring rain leak in one room. A portion of the drywall got wet, but not soaked, just streaks down the side. In subsequent storms, there have not been similar leaks. The wall appears very dry and has been since shortly after the incident. Can this drywall be painted over now, or must it be replaced/repaired? If it needs repair, how do I do this?

Generally you should be able to paint it if it looks and feels dry.
But you might want to wait for the back to be dry too, and that you can't tell.

Assuming that this wall was painted and the water was on the external surface you should be able to paint if the surface is undamaged and dry. Paint it and see what happens. What do you have to loose.
However, if you had a leak and have not found the cause and taken corrective action it will leak again.

I agree, good answers. I would prime with KILZ® General Purpose Interior Primer