Engine Smokes after turning the vehicle off. on 1995 Ford Explorer

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I just bought this vehicle even though it has 221,000 miles on it.
The oil pressure gauge was extremely sporadic. So much so, that I thought for sure it was a bad sensor and nothing wrong with oil pressure.
I checked oil level and oil was low, so I put in 2 quarts. The oil pressure gauge acts normal now and remains perfectly steady.
Truck starts easily and runs like a charm. It drives just fine.
I can drive 10+ miles and the temp is fine, oil pressure is fine, idles fine, nothing appears to be wrong while it is running. I can sit and idle for 3-10 minutes, NO smoke.

After turning the truck off, smoke will rise out of the drivers side of the hood. It doesn't do it long enough to open hood and locate the source. Occasionally, get an oil smell when it is smoking.

Any ideas/suggestions? There is some oil residue on the top of the engine. Maybe some degreaser to clean that up, and maybe it is just something on the outside of the engine?
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