UPDATE: With Opera 11.10 you can define your IMAP-keywords in the labels-menu. No need for the following workaround anymore.

1. Create your new label

Simply create the new label. But it will work with old labels too.

Synchronization will work without any effort if you edit the default labels. No need for the next steps then. Just take care that you edit the same on every installation.

2. Find your index.ini

Now you have to find your index.ini. It's located in the mail directory which can be checked on opera:about.

Close opera and back it up (your index.ini).

3. Find the right label

Open your index.ini and search for the name of your label. "Ctrl + F" helps. The part will look similar to this:

[Index 443]
Name=MyNewLabel
Id=200000001
Parent Id=1600000004
Mirror Id=0
Type=2
Keyword=
Visible=1
Account Id=0
Model Type=0

You may have noticed the "Keyword"-part. Set any value as keyword (e.g. your label name):

[Index 443]
Name=MyNewLabel
Id=200000001
Parent Id=1600000004
Mirror Id=0
Type=2
Keyword=MyNewLabel
Visible=1
Account Id=0
Model Type=0

Save the index.ini.

4. Set labels

Now start Opera and label some emails with the keyworded labels. If there are none just send emails to yourself and label them.

It will help you because once you open the next Opera installation it will find the labeled emails and create a label automatically. The name of the automatically created label is the value of "Keyword". So it makes sense to use your label name as keyword (like I did in the example above).
Of course you can edit the label names afterwards but you have to do it on every machine separately. Automatically created labels will not overtake your settings!...

5. Further thoughts

...But this also means you can synchronize labels (thanks to the independent keyword) and give them different settings and different names on different opera installations.

So you could create labels for several offices. "Office1"-mails will only be shown in office 1 and be hidden in office 2 and vice versa. The good thing: If you are in office 2 and need emails from office 1 - just click on the label.

Restrictions

Emails that already have been labeled before you added the keyword will not be synchronized. Unlabel them and label them again after you have set the keyword.