You are probably better off just laying the gun under the bed that a case.
Throw away all the 'oily rags' and get some RIG=Rust inhibiting grease and a RIG RAG (sheepskin) and wipe down after each handling and preiodically therafter. Could also take the oily rags to the shop and wipe down the wrenches/saws/chisels/ etc.
Im cleaning some guns for a friend whos house burned.The guns were not damage, by the fire but sure are corroded.
A spoonful of Rig applied to 8 of them would have done a world of good 10-15 yrs ago.
Oil on a gun moves esp when in a rack/safe of standing in the closet. At least 3 of the above 8 have 'black' stocks where the oil has run into the wood just below the barrel/reciever. It will never come out.