If it is just the oil with no pitting, you could completely disassemble it and put it in hot water with dawn detergent. Use a soft cloth or brush. Then remove it and rise it well with hot, hot water. Dry it completely, you can use a hair dryer, or even put the parts in an oven on low for about 15 minutes. Then oil it and reassemble.
Soap and water is not a bad cleaning soulution as long as you dry things well and oil when you are done.