a shortish bath (just the cages mind!) in some drain clearing gel or similar is great for quickly removing the outer layers of crud and oxidisation - dilute it 3:1 with some hot water and you can almost see the stuff come off (literally minutes is all you need)
however while it will leave a nice clean surface it won't polish them
It's a lot of elbow grease with sandpaper (or emery cloth strips are better for hard to get to places) I'm afraid, then some metal polish for a nice finish. If you can find a decent buffing wheel or suitable drill or rotary tool head then that might help, but its very easy to also screw up the finish with powertools if you aren't careful (NEVER use those harder grinding bits you get with dremels for example)
if the bolts and spindles have any rust then leaving them in a jar of vinegar over night is generally a good and cheap way of getting rid of a lot of that - again, use some metal polish to regain a nice finish
if it was me I'd just clean them with draino and accept a fairly 'rustic' surface finish I think - those V8s would be a total PITA to polish i think with all the nooks and crannys...