Managing personal Outlook.com account settings, security, and privacy
Ok, so I had the same issue. It was on Chrome browser. I could log in using incognito (private browsing), but not the standard windows. My friend could however log into his account without having the same issues.
Here's what I did, I had to turn off, "Continue where you left off" and it worked. Maybe the same might work for other browsers too.
So, it might not work for others, but it worked for me :)
Hope this helps