how do I get the oil base die out of carpet
I don't know if this will work but I tried it once on wax but try putting some paper towels over the spot then put a hot iron ,(not so hot that you burn thru the paper towel )but put it on there and let it set maybe the oil will heat up enough that it will absorb onto the paper towel--- it is worth a shot. if not test it first but maybe a diluted bleach water too.
I would call a professional steam cleaning company. (the sooner the better) if they have a Stanley Steemer in your area, I have found them to be very professional. You may make it set in worse by trying to remove it yourself.