I can't delete any of these actions. I did do Shift + X but they just keeps showing up. There's no O next to them:
Here's blend file:
I can't delete any of these actions. I did do Shift + X but they just keeps showing up. There's no O next to them:
Here's blend file:
When you delete an action, it still exists in Orphan Data:
Although ther's no O next the action name, it will be removed after saving and reopening the file.
If you want to delete all Orphan Data immediatly, just click the "Purge All" button.
NOTE If you want any orphan date to have a Fake User and prevent them to be deleted, click on the x:
If you want to delete a single action do it in the NLA Editor.

If you want to delete all actions, go to the Outliner and type animation in a search window. Hover your cursor as pictured below, press RMB-->Clear Animation Data. All your actions should disapear.

Probably best way is change Outliner into Blender File mode, right click on action and click delete.

The only reliable way is to delete actions via the Outliner while having it in Blender File mode.
So I found the solution I needed by accident. I was fishing around the the outliner after trying all of the steps above and stumbled on this guy
This was the action that I couldn't get rid of, either in the action editor or the NLA editor. I even tried the Purge All Orphan Data trick, and that did not get rid of this action. The only thing that did was opening up this animation hierarchy and deleting it from there. And finally it was gone.
Thanks everyone! I've managed to figure it out eventually! If shift+X cant remove the actions completely, you could do as Gonzou suggets to delete ALL of them.
To delete each of the actions, Go to NLA editor, delete the Action Stash labeled the name of the action you want to remove. Then you can Shift+X to remove the action completely in Action editor!