Hi, Carol. The old vertical radiators were made of cast iron which would rust if it did not have paint on it. The real question is how much paint is on them. Ideally, I think that it would be better to replace the old monsters with baseboard heaters but I know that this would be expensive and messy.
As far as stripping goes, the condition of the current paint would determine this for me. If the present paint is a reasonably good paint job, I would just paint over it. Since a lot of these were painted while they were hot with paints that are not as good as today's, a lot of them have paint jobs that are pretty runny and drippy. If you choose to strip, the best way would be to remove them and send them out for sandblasting. Admittedly, this would be a big job since they are bulky and heavy. The next choice would be a chemical stripper but the problem with these is that there are a lot of areas that are difficult to get to for stripping. If you have 66 kajillion coats of paint, Peel away is probably the best choice but, again,it is really difficult to reach into the narrow places. I have a thing about methyl chloride based strippers and don't think that they are safe for the user so my choice would be one of the non-toxic strippers. Again, this will be difficult to get deep into the inside areas. Remember that the older layers of paint probably have lead based paint. And don't forget your gloves and eye protection. Be careful around the bleeder valves so you don't clog them up worse than they already are.
Sorry about Mr. Punctuation and his language. I guess he thinks that he is being cute or something. We try to ignore him but I guess that this is one of the prices you have to pay for freedom of speech on an open board when anyone with $400 can get on line. He sure has made this board a lot less fun.