Steel wool or Naval Jelly, you can find them both at the hardware store. Naval Jelly might be easier on your fingers.

My dad taught me to remove rust with 3-in-one-oil and some very fine steel wool.

Yes, and not only does the steel wool remove the rust, the oil coating one leaves on the tool prevents more from occuring. It is one ritual I always mean to do each fall and seldom get to. I also buy a lot more tools than I should have to.

Can anyone recommend how to sharpen these shears?

Thank you everyone, I'm off to clean tools. Britania, if you have the same all-metal, one-handed shears I do - they are self-sharpening.

leevalley.com has a special little gadget just for sharpening pruners, etc. It's neat, effective, and not too expensive :)

Here is a link that might be useful: sharpener