Wire brush and/or scotch brite pads.

Bigger question may be what do you coat the parts with before storage? I've seen threads on the topic, maybe you can find one. I might douse everything in WD40 and wrap in heavy paper, oxidation or not.

In the words of the great Traveling Wilburys,
"Some places they get mildew
And others get too hot
Some places are so damp that
Everything you got just rots
All kinds of condensation
A direct result of rain
They're not much compensation
When everything's been stained
Some have sentimental value
That cannot be erased
Go store it in a cool dry place"
--
XC60 / Odyssey