Aaargghh! A little knowledge is a dangerous thing. Some good advice here, some bad.
First, you don't know what you are dealing with, and neither do we. That makes all advice very hypothetical, and potentially dangerous. Short of a chemical analysis, you are "shooting blind." However, there is a safer way to do this.
First, try Simple Green™. Full strength, just soak 24 hours and see what it does. It will remove baked on automotive oil residue. NOTE: do not use on aluminum or aluminum alloys.
Second, try Goo Gone™. Apply, soak for a few minutes, wipe. This stuff seems to remove most hydrocarbons, some take more time than others. FLAMMABLE. ADEQUATE VENTILATION NECESSARY.
Third, try ethyl alcohol (Everclear). FLAMMABLE. ADEQUATE VENTILATION NECESSARY.
Fourth, try isopropyl alcohol, 90%. FLAMMABLE. ADEQUATE VENTILATION NECESSARY.
If none of the above work, you have entered the realm of truly hazardous substances requiring adequate ventilation, solvent-proof gloves, and a face shield as minimums. "Lacquer thinner" is a blend of various solvents, and thus will dissolve quite a few organic compounds.
A very low toxicity substance for removing the last residues: creamy peanut butter. Peanut oil is "nature's penetrating oil." Slow, but effective.
Regardless of what you use, it is wise to treat all hydrocarbon solvents as potentially toxic. What you are not exposed to cannot kill you. Lastly, "safe" does not exist, only "safer" and "less safe."