How To Fix 404 Errors After Changing Categories

Surely this is covered somewhere, I just can’t find it.

I cleaned up the categories on my site, creating new categories and reassigning existing posts using the Simple Tags plugin. The 404 Notifier plugin lets me know every time a search engine bot fails to find content under the previous categories. Tried to install the Redirection plugin to stop the 404 errors, but installation fails, resulting in “Plugin could not be activated because it triggered a fatal error” messages. I have about 6 categories that should no longer exist, yet they still return 404 errors when the bots find them. How can I (1) eliminate reference to the obsolete categories so the bots don’t search for them, and/or (2) redirect the 404 errors to an appropriate category page?