If doesn't matter if you dropped your phone in motor oil or olive oil, restoring the phone will be a major challenge. Unlike water and other basic liquids, oil has a way of creeping into all sorts of places on the phone, and it doesn't evaporate or absorb out easily. It will roll around the interior of the phone, wreaking havoc on your speakers, LCD and internal components, so removal is a necessity.
Oil vs. Water
The difference between oil and water when it comes to phones is that oil does less harm to electronic components. The smoking point for most oil products is higher than your phone temperature will ever reach, and some electronics can continue functioning with a little oil present. It does present more harm to your LCD and ports, however.
Turn off the phone and remove your protective case. Use a soft cloth or cotton balls to remove all oil from the exterior. Cotton balls are excellent at absorbing the spots where oil is really prevalent. If the oil is not wiping off easily, try absorbing it with a paper towel. A wet wipe or other alcohol-based cleaning wipe will help break down and remove oil from the exterior. Take your time, using cotton swabs and Q-tips to remove as much oil from the exterior as possible.
In a cold climate, the oil will solidify. Use this opportunity to scrape away oil with your fingertip. This works especially well on coconut oil and cooking oils. Motor oil will not solidify in the cold. Alternatively, place the phone in direct sunlight or over the defrost on your car heater to liquefy the oil while using paper towels to absorb and wipe it away.
Interior Oil Removal
After all the exterior oil is removed, you have to deal with the oil in your phone screen and speakers. Try removing the battery and placing both the phone and battery in a bag of white rice for several days. Place the phone upright so the oil can drip down and be absorbed out the charging port.
If the rice fails, try the same process with cat litter. Leave the phone in the litter for at least a full day. This process works well for water and can work for oil, but it's not a guaranteed fix. Replace the battery and test the phone. You'll know quickly if oil remains in the screen and speakers.
Replacing Phone Components
Before you attempt a fix, try testing the warranty service on the phone. A previously purchased insurance policy might make you eligible for a replacement. If the warranty has expired, the oil will not pull away and your phone remains compromised, the best course of action is professional repair.
Replacing the screen is a viable options. Speaker replacement can also work on some phone models. A professional repair shop is the best route when the oil refuses to leave your phone.