Honda Accord doesn't start when it's raining

I have a 87 Honda Accord (4 door), 244k, and I honestly don't know the engine size-it's not printed anywhere on the engine or under the hood. I have owned the car since May/2007. Everytime it rains, the car doesn't start or if it happens to start it's all sputtery and doesn't stay "running" long. It has had a basic tune up, but I do know the distributor cable/plug wasn't changed. I have had my "charging" system tested for free and it showed no problems. As far as any leaks, it has a power steering leak and smoke comes out from under the hood when driving it (doesn't have an oil leak, just is burning it). I would appreciate any help you can provide, and I will do my best to provide any additional info you may need.