Also, what are your settings for 'When I mark a message in IMAP as deleted:' and 'When a message is marked as deleted and expunged from the last visible IMAP folder:' in Gmail settings?
They are not gibberish and come from a news agency I subscribed to. The headers are thusly
There are List-Id headers in them. A List-Id header tells Opera to create a mailing list view for the mailing list. So, it's not a bug and is intentional by Opera.
Close down Opera and delete autosave.win in the sessions folder in the preferences folder. See "help -> about Opera Mail" for the location. If that doesn't work, rename operaprefs.ini. If that doesn't work, check the properties of the opera mail shortcut to make sure the command is correct (as in, path to operamail.exe).
You can turn on logging for the account. But, I'd also retype the username and password on the "Servers" tab in the account's properties. Also, make sure the TLS and port setting are correct.