Oil can be separated directly via decantation. However, alcohols including glycerols are soluble in water. Hence, you could try mass transfer operations such as azeotropic distillation, given that you know the type of alcohol impurity present in the mixture. Glycerol being alcohol will also be removed during the process.
I agree with RJ Robert that free oil shall be removed first by floatation (light oil) or decantation (heavy oil) and that the alcohols and glycols are soluble in water.
These water soluble organics are fully biodegradable by high-rate anaerobic digestion (HRAD) as proven in full industrial scale HRAD plants worldwide since decades. HRAD converts the soluble organics to biomethane at up to 99% efficiency. This biomethane can then replace fossil fuel to produce heat (e.g. steam) and/or electrical power while reducing CO2 emissions.
If interested I would be happy to provide you more information via email.
Seemingly this RG discussion may possibly help: https://www.researchgate.net/post/What_is_the_easiest_quickest_and_cheapest_method_to_separate_water_from_dilute_glycerol_solution