While investigating Skype login problem, Microsoft support made some changes to login service and after that the situation escalated and now all students are unable to login to any Office365 services. We have asked Microsoft to raise priority on this support process.
At the moment we do not have estimate how long it takes to fix this, but we have contacted Microsoft and they promised to try and get back to this later today (tuesday).
Update 14.12, 8:20:
Mobile device synchronization should work if the client does not require separate authentication.
Logins to Office365 portal does not work, but you can still use traditional Outlook desktop client (installed on all JAMK workstations) or 3rd party email software that supports old IMAP4-protocol.
Update 14.12, 14:00
Logins to Office365 portal works now. Issue with Skype login is still under investigation.