I still doubt that what's coming out is really oil. Pure oil in the stool would mean there is no bile for emulsification of fat. This in turn would make other symptoms like ingestion, feeling of being full and bloated and most of all clay coloured stool.
I am inclined to think that the mucous linigns secrete liquids in an increased amount in order to shred off toxins. Maybe you want to check furthe whether it is oil ore something else.