I am having the same problem as ACL8150 on my Samsung Galaxy S4 and my Samsung Galaxy Tab4 beginning about two days ago (17th April 2015).
The authentication error started after accessing the website resulted in my having to change my outlook.com password and activate two-step verification there.
Access to my outlook.com email account from the standard Android (Google or Samsung)-supplied Email app which had been working fine until this time.
I deleted my outlook.com account from the Email app on my phone and tried to add it in again. This tells me that the server password that I'm using (I'm trying to use the account password for my outlook.com email - which still works fine via my computer)
So different servers are used for access to outlook.com email from mobile devices. In this case it appears that it/they are out of sync with the computer access server/s in some way.
The same server password problem is occurring on my Samsung tablet (from the same time), i.e. unable to connect to my outlook.com email account.
I found http://windows.microsoft.com/en-au/windows/outlook/to-go and saw that the server name is now s.outlook.com (I had been successfully using h.outlook.com (?) on my phone and am using Exchange server bay405-m.hotmail.com/Microsoft-Server-ActiveSync
on my tablet).
So somehow I am no longer able to access my outlook.com email from my mobile phone or tablet.
I would appreciate being able set up my outlook.com email on both of these devices so any assistance that you could provide would be appreciated.