The phrase "oily mess" means a situation or thing that is greasy or covered in oil, which can make it messy, dirty, or difficult to clean up. Full definition
I have super oily skin, so by the end of the day I am a total oily mess. (southernbeautyguide.com)
Plus all that oily mess really gets one in the creative groove! (creativejewishmom.com)
I just tried an almond flour recipe from a new and very popular cook book and it was an almond hockey puck like oily mess that I threw out. (kingarthurflour.com)