There's a lot of great suggestions in the replies. I haven't tried them (except chrome polish, which worked okay). I'd try the soaking solutions if your parts includes threads, areas that are difficult to get to, or parts with irregular shapes.

That said, I have had great success using electrolsysis to get rust off parts. There are plenty of tutorials on YouTube. There's a bit of setup involved, but its results are spectacular.

$.02 to ya

I use dawn mixed with barkeepers friend. Put everything in a bowl with the dawn and barkeepers friend, then I sit a vibrater on it. The vibrater agitates the screws and they rub against each other and come out fabulous! I use a polishing wheel on my bench grinder with a fine polishing stick to polish chrome. Works very well, except my grinder shocks me when I touch it! Kleening