I soak and rinse in detergent too, and take to it with an old toothbrush. This will remove all the crusty soap scum that has accumulated.
I have also used a brass brush to remove some stubborn corrosion. You want to be gentle with this though, and make sure it is brass, as steel brushes will scratch the crap out of your razor. Bunnings sell a pretty decent 3 brush set, containing nylon (good to use instead of a tooshbrush), brass and steel. I don't use the steel, but the nylon and brass are great.
Then, finish with autosol (also at Bunnings) to bring back the shine.
I've heard of some using superfine steel wool, but I haven't used that myself.
If the plating has gone, then there is nothing that can be done besides a complete replate, but that isn't worth it IMO.