If the oil is electrically charged, then yes, something with a charge of the same side will exert a repulsive force on it. The question is whether the force exerted by the electrostatic charges will be sufficient to overcome the adhesive properties that oils possess chemically, which is why oils ordinarily stick to things.

Will the charges inside of the oil be free to move within the oil? If so, then you might get fractionation of the oil containing the charged particles inside of it, versus the oil that doesn't. The oil that doesn't will not be repelled by an electric field once it is devoid of charge.

Also, how do you get a charge in oil in the first place? I am not familiar with the Millikan oil drop experiment, but I do know that charges by definition make polar molecules, and oils are inherently non-polar. I can imagine doing it by putting in iron filings or something similar, but they're going to be able to fractionate as I said above. You could also use phospholipids, but then you might have other problems of how you keep the charge (and they too would probably be able to fractionate, depending on the temperature and viscosity of the oil).