Hi Johan,
To troubleshoot this issue, it is suggested you try the following steps:
1. Check whether you have activate two-factor authentication. If so, try de-activating it and check again.
2. Try change the Region settings in System Preferences to United States under System Preferences > Language & Text > Region (tab):
3. Make sure you choose the following option to sign in with your organization or school account.
4. Try uninstall the Office installations completely and then reinstall.
Here is a related thread for your reference:
http://answers.microsoft.com/en-us/mac/forum/macoffice2011-macstart/mac-office-365-not-activating-with-error/b4fe581a-198e-4ed0-92db-5a1914839e9e
Please let us know to help you further if the issue still cannot be resolved.
Thanks,
Eric Yang