You really should start with a fresh profile since things sound pretty messed up. If you're using Opera Sync though, when you log back into Sync, if your sync data on the Sync server is messed up, it could trigger the problem again. If that's the case, you'll need to reset your sync data at https://www.sync.opera.com/ and start with a new profile again.
If you don't want to do that, you can try to fix the speed dials yourself. Goto the URL opera://about, take note of the "profile" path, and close Opera. Then, delete your "Bookmarks" and "BookmarksExtras" files. Also, Delete any Bookmarks.old files you see. Then, that should hopefully fix things as far as speed dials go. If you're using Opera Sync though, that might complicate things and might remove all speed dials from the Sync server.