Are you using Exchange online, for emails? Then I recommend you to refer the following URL.
https://learn.microsoft.com/en-us/exchange/back-up-email
Basically Microsoft takes care of the backup and its retention, however if you still want to backup emails in Exchange online, there are commercial tools available and those tools support backing up data to Azure. An example of such a software is given below.
https://www.acronis.com/en-gb/solutions/backup/cloud/
With regard to Onedrive, there is no direct option available right now in Azure backup that can be configured with these services. One thing you can do is that you can sync one drive to your local computer and use Azure backup to backup the folder. If you decide to backup emails using commercial software, they mostly support onedrive too.