apart from the idle air control valve I would say you should check the distributor for cracks. You stated it happens when it rains. GF had the same issue and I replaced everything before I figured it out.

Here it what you can do:
You will need a screw driver with plastic or wood handle (just not metal)
Gloves (further safety)
A piece of wire
Tape
Spray bottle or water bottle with a hole in the cap and water in it

1. strip one end of the wire and wrap it on the metal shaft of the screw driver. Tape it to secure it.

2. Start the car and observe idle.

3. Put the gloves on and hold the other stripped end of the wire to a good ground (preferably your battery)

4. Probe around the distributor and spark plug wires. If there is a crack in either that you don't see, it will show up by killing / affecting your idle.

5. If you find nothing, spray water on the distributor and observe idle. If it affects your idle then there is a crack... probe around and it will affect it even more.

6. do the same for your wires.

So recap... If there is a crack in either that you can't see, the current flowing through the distributor or wires will arc onto the grounded screw driver.

Good Luck

 

Alright, I will check this. I believe it has a new distributor in it; and I believe we have changed it out another time in the last 6 years.

 

Wait a minute.
-Are you saying there is oil on the tip of the plug (aka your motor is burning the oil off). When you say beneath the rocker arms are you refering to the valve stem seals? If so I don't understand how it is on your plug wires.
- If it is on your plug wires then from where and what part of the wire? If it is the part of the wire that goes into the boot and touches the plug then that means you have an oil leak between the valve cover and the spark plug tubes. If this is the case then it will cause a misfire on that cylinder or random misfire if it is more than one. This is because the oil shorts out the connection from the plug boot and the plug. therefore current isn't directed to the plug and you have a poor spark or none at all. No spark means no burn. No burn means rich fuel smell. Take the spark plug boots out and look in there for oil. You can also swab your finger around the tube and see if you get oil on it. If so, change the valve cover gasket and all should be fine.

Have you washed the motor before? I know washing when its hot helps everything evaporate but the extreme temp changes can cause cracks in older plastic parts. I would put money on the valve cover gasket though... if oil is there.