I have read some other posts and I am thoroughly confused. Here is my setup, and what I would like to do: I have a subscription to Office 365. My main email account is a Gmail account, and it´s a POP account. I also use Calendar, Notes, and Tasks on my Outlook 365 setup on my main desktop computer. I also have a Laptop that I only use when I am on travel. Therefore, I never use the Desktop and Laptop simultaneously; I use either one or the other.
Let me assist you with the issue.
It is not possible to have the .pst file saved on One Drive and then shared on two different machines.
However, in your scenario, the best way to sync your email account is to setup the email account using the IMAP protocol.