A Microsoft file hosting and synchronization service.
You can open a OneDrive file to work on it while offline. When you reconnect to the internet it should sync up.
I suggest you work on the file while it is in your OneDrive folder. Don't remove the file from OneDrive and then work on it.
Files on your USB drive are not OneDrive files unless your OneDrive folder is located there.
You can replace the old OneDrive files with the newly updated files. This is especially easy if they have the same name.