What is the best way to get the rust off these oil spouts??
I doubt those spouts were anything but straight metal types to start from the looks. Chemical treatments like described will work especially for the knurled lid portions.
0000 steel wool can be used initially to determine how bad the metal is pitted. We use to use naval jelly all the time to clean smaller metal parts, very caustic though so wear gloves and clean the piece after using.
I'd dust them with a quick coat of sealing primer once you use whatever technique to de-rust them. Then you can paint them to your desired matte color when you're ready
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