I don't use One drive, but I suspect that the method is similar to using DropBox and Google Drive. These apps on Android do not fully synchronise files, but only let you access files remotely. OpenSongApp is designed to work in offline mode and Android's storage method doesn't let you access remote storage folders and files on cloud services for full write permissions (when my app asks you to set your OpenSong/ folder the first time you ran it). This avoids me insisting on users having Google, Dropbox, OneDrive accounts, etc. and internet access for usage.
This app actually synchronises a remote folder (OneDrive) with a local folder on your Android device. If your OneDrive folder already has an OpenSong/ folder (which contains the Sets and Songs folders amongst others), make sure you use the OpenSong/ root folder for the local and remote folders. That way songs, sets, etc all get syncronised.
Make sure to make a backup of your files before you start. Remember you should sync the entire OpenSong/ directory for your online folder and Android folder.
Hope that helps?
Gareth