It sounds like the engine is lacking air at idle. The IAC should maintain the engine speed at the programmed target idle UNLESS the PCM has applied the maximum programmed IAC steps.
The other, often overlooked, source of idle air is the PCV valve. The system is designed to regulate idle air but relies upon the correct volume of air being applied through the PCV. The IAC simply supplements that air with intake air.
I would suggest a thorough cleaning of the throttle body, IAC, IAC air passages, and PCV valve and hoses as a start. Inspect all other hoses for damage while you're at it. A faulty PCV valve/system will also fail to remove moisture from the crankcase through normal operation, and this can appear as moisture in the oil, as you reported.
If that doesn't improve the condition, connection a scanner to read the target idle, mixture, and IAC counts would be helpful.