It would be a good idea if when the app is set to not use mobile data that it not use mobile data. My phone blew threw 300MB a day on two different occasions while I had both the OneNote app and the Android settings set to not allow this to happen. I opened the app, changed 1 line of text, and whoosh, 300MB gone off my data plan.
I uninstalled the app, cleared the cache and tried installing it fresh. Triple checked all settings. Worked great for a week and then woosh, 300MB gone again. At this point, I'm using Evernote because I can no longer afford OneNote.