That depends on what the inorganic and organic material are. The order I would try is surfactants, then solvents, then some form of reactive chemical treatment.
If the surfaces are accessible, just adding something like dishwashing detergent to the surface, rubbing it with a soft brush, and then washing it off with water will remove most tarry or sticky organic materials.
If the surface of the inorganic material is sensitive to brushing, dissolving the organic material in a solvent like toluene, hexane, or any of the various commercial oil paint brush cleaners usually works. Sonication may speed this process.
Finally, if nothing else works and the inorganic is inert, soaking the material in chromic acid cleaning solution or a concentrated sulfuric acid cleaning solution may degrade the organic material to the point where it will fall off. This was particularly useful for cleaning stubborn deposits on laboratory glassware, until it got so difficult to dispose of the extremely toxic and reactive waste.