This may sound like a silly question, but how do I completely delete actions?? Not just unlinking them from an object, but actually deleting them…

Not silly at all. It’s a bit obscure:

Shift-F4 to open a Data Selector window.
Find the Action library (may have to browse up through the tree by clicking the dot-dot).
Left-click on Action to open the library.
Right click on desired action to select it. Use F key to toggle the “fake user” (F) flag off (or on, if desired). Repeat as necessary for other actions. Any action with an F gets saved; those without are deleted in the next steps.
Click Data Select when done.
Save the file.
Reopen the file. Actions from which you removed the F flag should be gonzo.

Too bad it’s not as simple as clicking the F in the materials panels.

Wow…thanks!! I would have never done it!!! I was going crazy, thanks a lot!!