Alright, I believe I have good news. I was told that the oil was recently changed in the car when I bought it, but no dice. I think you guys are right and what I was seeing was probably just old moisture from it sitting for a long time. When I drained it the pan, there was a brown tint to it, but nothing that seemed like a significant amount of water or antifreeze. The filter on it also appeared to be ancient. So the combination of new oil/ new filter has seemed to alleviate a lot of the white smoke and hard running problems it was having.
There does appear to be a small oil leak from both the valve cover gasket and the head gasket, so I'm sure replacing those is inevitable, but for now the eagle will live to drive another day