If you just want a no-nonsense way of fixing it, start with a new profile. Goto opera://about and take note of the profile path. Close down Opera and delete that folder. Start Opera back up and it'll be like new. That should get rid of the demons. You'll lose all your settings, bookmarks and passwords etc. that way of course, but it'll sort things out.
Do you use Opera Sync?
If you don't want to fully wipe your Opera profile, you could goto opera://settings/siteData and delete all your cookies. And, you could goto opera://settings/clearBrowserData, switch to "advanced", set range to "all time", check everything but your passwords (or that too if you don't mind) and clear. And, you could goto opera://settings/reset and reset Opera.