All the chrome work can be stripped off and soaked in a mix of oxalic acid for 12-24 hourshttp://www.ebay.co.uk/itm/500g-Oxalic-a
I second that. There was a thread about removing rust from chromed parts where the oxalic acid was mention, I tried it myself and it does wonders.
Regarding rims I have a similar set of chromed steel Rigida that I cleaned using kitchen aluminium foil and water, but it took a lot of time and effort. You can check the photos here: https://picasaweb.google.com/1005210978 ... directlink
Maybe you can try it: take a piece of aluminium foil and make a ball of it, wet it in water and rub the rims. Or if you have a container big enough, you can try oxalic acid method.
I ended buying aluminium Weinmann rims anyway, but I used these Rigidas for a year on a daily basis.