How can I strip and repaint an old radiator?

A good quality scraper and elbow grease. A palm/ orbital sander probably save some of the physical labour.

Using a combination of paint remover and a consumer grade sandblaster can help reduce the amount of work you need to do to remove the paint in tight places. Soften the paint with the stripper then let use the sand to lift the dissolved paint. This can affect the surface finish of the metal so manual scraping and wire tools are also a good option. I'd suggest testing your process on an inconspicuous area first. Sometimes radiators end up with layers of latex on top of oil based paint so you might find that using 2 types of paint strippers are necessary and always be aware that lead paint can exist in old paint finishes. Proper safety equipment should always be used and preparing your work area is important to prevent contamination to people and the environment. If you have lots of radiators it could be worth while have them uninstalled and then send them to a shop that provides paint removal as a service.

For the corners and tight spots, a small wire brush or even a toothbrush works really well. You can also use steel wool or a detail sanding tool to get into crevices. Make sure the radiator is completely dry and free of dust before repainting. Use a high-heat primer if needed, and then finish with a radiator or enamel paint designed to handle heat. That will give a smooth, long-lasting finish.