Just to bring it on home. The Skydrive app is broken as of right now. There's no way (including using the "app password" option) to make it sign in.
To keep using the linked Microsoft account (mail, integrated SkyDrive, Office, etc.) all you have to do is sign in using IE on the phone and check the option to trust the device. Then sync the account and it all should be fine.
The SkyDrive app is different to the SkyDrive integrated into the phone. As that goes through your MS Account. So even if you can't use the app you can still upload/view photos, docs, etc.
I hope I was of help.
Much Love!