The two oils I have used are knight gun oil and Breakfree CLP. It sure frosts me.
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Baking Soda in warm water neutralizes the rusting process. Give it a good scrub down, clean it again and then oil it. Also, do not use a WD-40 type of penetrating oil. This will actually remove rust, and as stated above, blueing is a rust process hence it will slowly remove the blueing too.