Lamp oil may be kerosene, paraffin or a vegetable oil, such as corn oil or olive oil. Some lamp oils have coloring and/or scent added. No matter what lamp oil is made of, spill clean up is the same. You should act quickly, especially if the oil is colored and spilled on carpet or fabrics, to prevent stains and avoid a fire hazard. Many non-kerosene lamp oils have a high flash point, which means they won't spontaneously combust; however, the oils are flammable.
Immediately confine the spill by covering it with clay cat litter if the spill is on a solid, non-carpeted surface. If the lamp oil spilled on carpet, blot immediately with disposable rags or paper towels--don't push it further down into the carpet, however. (If you don't have any cat litter, use paper towels to soak up the spill.)
Put on rubber gloves, and place the oil-soaked rags, paper towels or cat litter in a trash bag (scoop up the cat litter with a flat piece of cardboard or plastic).
Mix liquid dish detergent and warm water in a bowl or bucket. Whether you need to use a bowl or bucket depends on the size of the spill. For the detergent solution, Stainmaster.com recommends using 1/4 tsp. dish detergent per 1 cup of water.
Wet a disposable rag or paper towels in the cleaning solution, and apply to the spill. The detergent helps thin the oil, allowing it to be more easily removed from any surface. If you apply this to carpet, all fibers should be soaked with the solution, but try to avoid wetting the pad beneath the carpeting (this isn't easy). Don't press the rag down heavily onto the carpet--this forces liquid down--and don't scrub carpeting. Blot it gently.
Alternate dry rags or towels (to soak up the oil that the detergent solution loosened) with wet, soapy rags or towels (to apply more cleaning solution). Do this until the oil is gone from the surface.
Use a towel or clean rags, soaked in cold water, to rinse off the detergent solution. Allow the area to air dry. Dispose of oil-soaked rags, paper towels and other materials according to your local municipal waste laws.