Kevin,
You should never use oil on a rejector!
The dirt from the coins will eventually gum it up and make it sticky.
The only thing I ever do is use a little powdered graphite on the coin cradle and oversize guage (if it has one).
I take them complete apart to clean them. You can run it through the dishwasher, but take the cover plate off - it is the one with the decals secured by a 6-32 screw and a 6-32 nut. Take the 5 cent magnet off (1 screw) and prop open the scavenger plate (spring loaded piece)

Here is a couple of tips:
1. Make sure the nickel anvil screws are tight - two 8-32 screws on the back next to the triangular access hole.
2. You can take a pipe cleaner with rubbing alcohol to clean under the magnets - bend it in half and then like a hockey stick.
3. Sometimes the scavenger plate needs a little tweak.

Where is the coin(s) getting stuck?

Post a pic or something and I'll see if I can help.