Did you try making a new app password from your outlook/skydrive account? I've been doing the multi-factor for a few months and have been surprised at how many native MS programs aren't compatible with the multi-factor authentication. I've had to create an app password for my WP8 email/skydrive sync, my desktop one-note sync, and xbox live login among other stuff.
So if you haven't tried this, all you have to do is log into your skydrive/outlook web account, get into "account settings" (click your name, not the gear icon that indicates settings for that page). On the list of options, click "security info", see the heading of "app passwords", click "create a new app password". Type that random gibberish into whatever app is refusing to connect, done.
I've been using this for months and it works well with some annoyances. If I'm wrong then please someone give me a head's up. There's no way to see the list of things that are connected via app password. If memory serves, I can see this list on google and individually manage them like killing individual ones for a reset. On MS, my only option appears to be "remove existing app passwords" all at once as an entire group. Therefore if I have a problem with ONE password and need to re-establish it (which happened yesterday with my one-note sync), then I have to kill ALL my passwords and tediously renew app passwords for all my stuff on every device that accesses them (3 different devices for my pc one-note sync alone).
Doesn't happen often, but pretty annoying since typing in a 10 digit randomly generated password that you have to get through your laptop into your phone and xbox is pretty annoying when you've put your stuff away for the day and just want to watch a show on Netflix.
Maybe I'm wrong and that you can refresh just one by simply making a new one and the run and logging in with the new one without first killing the app password (again, all of them or none of them). I vaguely remember this being the case so far. But over the past two weeks I tried about 20 times to get my one-note to sync right via all sorts of workarounds I've came up with and the ONLY way I was able to get it to work this time was to nuke ALL my dang passwords. Now the next week or so will be filled with generating and typing in new passwords to everything on all my devices. But hey, at least I'm secure.
For the record I do love One-Note and wouldn't go back to Evernote. The whole reason I added multi-factor to outlook and gmail was a direct result of Evernote's accounts getting hacked in the spring and then one of my emails got hacked from that. So often I will remind myself that I NEVER had these stupid log-in issues with evernote but then I remember the hacking incident and remind myself of the trade-off.
Sorry for the rant but there's your answer!