I'm always getting oil and makeup on my home phone. I just wiped it down with some antibacterial gel and a paper towel, and it came out clean and shiny.
I've been through so many nasty phones. Often they are attached to an answering machine, and grubby hands/fingers leave a grimy or germ infested "Cold and flu machine"! I've been using the cleaning solution of either alcohol or (yes, this DOES work) finger nail polish remover and cleaning the phone with Q-Tips in the small areas. If you keep it up often, it's not ever REALLY bad.
After it is clean, spray it with some "anti-bacterial" spray. You are set to feel like you've avoided a bullet (colds, flues, etc.) by doing these steps every 2-5 days, depending on your phone's usage and your households members!
Cleaning Phones