Whamb has a preference button to associate itself with the appropriate things. I'd already clicked that. When I got to the File Helpers in IE, it was already in the appropriate places. However, it still opened in iTunes. Then I noticed that many of the involved mime types were set to download only, so I changed them to play with Whamb. That led IE to still open them in iTunes. Then I noticed that it had before downloaded .pls files, which were still Finder-associated with iTunes, so I changed that to Whamb within the Finder and it started working. Then I had to add Whamb to the acceptable programs to start within OmniWeb and everything was good.

Thanks for finally pointing me in the right direction. It would appear that there are many databases in MacOS X, some of which are now apparently deprecated and unused. I still think it ought to rely on mime types and not filename extensions, but maybe it does, even though I can't see that info in the Finder.