"Oily" is a good thing. No matter how hard you wipe the parts (with a dry rag-no solvent), there should still be a thin film of oil/paraffin on the surface. The "film" is what protects the surface from moisture.
For parts that will be on the shelf for awhile, I spray a rather heavy coat of T9 on the surface and allow them to air dry. The paraffin rises to the surface to form the desired moisture barrier. Just prior to installation you can spray the parts again and wipe them (or not).
Remember, the parts were oiled from the factory.
Frank