How to clean bathroom "overspray"?

In both my bathrooms, I have "overspray" on the cabinet doors and the bathroom doors (both painted and stained). I don't think this is hairspray, but rather those styling gels that spray out. It is sooo hard to get off, I have to scratch each blob (millions of them!) with my fingernail to get them off! I've tried 409, etc. and nothing seems to work. I let it soak, to no avail. Does someone have a product to suggest that will cut through this gel gunk?

Thanks!!