I want to say Tom's Secret Formula natural bio degradable oil, but the name eludes me right now, bought it at Canadian Tire. It's an aerosol spray oil that is non toxic and is food grade. I use that stuff to keep my steel plate from gathering surface rust.
I just use the food grade oils since I don't want the toxic stuff rubbing off onto my clothes or me while I'm wearing any of my harness.
You could soak your chainmail in a degreaser but be prepared for it to flash rust until you can recoat it with something. I think the easiest way to strip the oils off of it would be to use a dish detergent in the bath tub. Wear gloves as it will dry out your hands pretty good. Olive oil and baking is one way to season the metal, or any natural oil for that matter. I do that with the cast iron fry pans all the time after washing.
Could also toss it into a bag with sand and throw it around, it'll polish the links and get rid of most if not all the rust.