If it really is oil and not varnish then you will probably never get it out without aggressive sanding. It is not the oil that is the real problem, but the dirt carried into the grain by the oil. You may find using a chemical stripper useful as well as scraping to clean the surface, but you will probably be left with a mottled uneven finish, depending on what wood is underneath. If it is veneered ply do not sand too much as you will probably go through the veneer. Oxalic acid will help remove residual dirt and give you a more even colour, although if you are going to paint rather than finish bright you don't have to be so careful. Experiment in parts that will not be seen before tackling the main parts.