They make washable cabin filters so yes it's likely you can wash it. I would not oil it, even if they state to do so. Who wants oil vapors coming into their cabin? Then again I would never use a K&N for a computer controlled engine either due to any chance of fouling sensors. I know, they claim they won't, which is contrary to science. If you can smell an oil, it is releasing air borne vapors.
However, you can vac out pretty much any cabin filter unless you have respiratory problems that make every last micron count (or it has molded and it's not worth considering) but you can't get back active charcoal by washing it. Some say you can reactivate charcoal by heating it but it will never get back the original surface area, will always be less effective than new.