1-Soften it up with a squirt of WD-40 on each eylet.
2-WalMart Rust Remover 5.77/bottle, and a toothbrush or q-tips.
3-Apply liberally to each eyelet. If the Rust Remover sits too long on anodized rims, it'll lighten them up a bit, so be careful.
4-Usually 10 minutes will work. I often let it sit 5 minutes, then lightly rub with 0000 steel wool on each eyelet. BigPolishJimmy's idea of the dremel wire wheel would probably be quicker.
5-Two applications will generally take care of it. I put some of the rust remover in a small cup and use q-tips to get inside each eyelet (unlaced rims).

I've done two sets like that, working on a third, which was a lot worse. They eyelets came clean, and I'm slowly removing the ano with EZ-Off, then I'll "khatfull" the rim with varying grades of sandpaper and have polished rims, stainless spokes and polished hubs...on a $50 frame. But it's fun.