For your IMAP accounts, is there a webmail interface where you can set up server-side filtering to filter messages into IMAP folders? If so, that'd be a great workaround.
Another thing you can do is make use of IMAP keywords. In a label's properties, you can set a keyword (use only a-z and _ and no spaces and give it the same name as the label). Then, when the label's rules grab a message or you manually put a message in the label, that flag will be set on the message on the server. Then, if you access the IMAP account with another Opera, a label will be automatically created for that keyword. You will have to add the rules to that auto-created label though.
Keywords work in Thunderbird too with tags. When you apply a tag to a message it gets the flag. Opera will detect that and create a label for it. In Thunderbird, you can create a filter to automatically apply a tag to a certain message. Thunderbird doesn't auto-create tags when it detects a new keyword though.
To make an Opera label act like a folder, you can set "hide these messages from other view" in its properties. In Thunderbird, you can choose to view only messages with a certain tag.
So, keywords can kind of work if the server and the clients support it. Messages won't be moved to different folders, but supporting clients might have views for each keyword. You should even be able to manually move messages to different IMAP folders and keep the keywords. Not sure what mobile IMAP clients support keywords though.