If you are sure it is oil then it has to be coming out of the gearbox. Machine will have to be dismantled & gearbox removed to replace the oil seals & refill the gearbox with fresh oil. It may be just black marks coming from a build up of old soap & softener. Best way to get rid of that properly is to get the inner drum removed & all build up scrubbed away. Anything else doesn't really get rid of all of it.
Lincoln Appliance NZ, February 2011