What is the best way to clean immersion oil from the microscope lens?
In my experience, any microscope worth using has a minder. I would strongly suggest finding that minder, their opinions about cleaning practice should be respected. Objective lenses can be very pricey so they should be handled with care.

Detergent or water are inappropriate for an oil immersion lens. Detergent is likely to damage anti-reflective coatings on the lens. Water doesn't mix with oil.

My standard procedure with oil objective lenses is to wipe oil off with a good quality lens tissue (Kodak). Do not use facial tissues or a lab tissues, such as kimwipes. They are too abrasive and may sractch the lens. If someone has allowed oil to dry on the lens, I take care to know what solvents are correct for the lens and oil that are being used.