How to prevent users saving to onedrive

Sorry, not a proposal to solution, but what bad decision to do it company wide. There are tons of policies to make Onedrive really secure place to store and access documents from managed devices.
From various experience in the different companies I could say that forbidding something is not an option at all, you will forbid controlled Onedrive, unmanaged tools like Google drive, Dropbox, Box will come into the play where you won't have any control of and that will make things even worse.

One of the examples is to forbid file download \ printing \ syncing from unmanaged devices by creating such policies.
https://docs.microsoft.com/en-us/sharepoint/control-access-from-unmanaged-devices

In addition to this Onedrive probably has the best sharing options between the business units, companies etc.
https://support.office.com/en-us/article/share-onedrive-files-and-folders-9fcc2f7d-de0c-4cec-93b0-a82024800c07
https://docs.microsoft.com/en-us/sharepoint/external-sharing-overview