Hi,
I would not access the PST file from different machines, its not a recommended practice.
Office 365 will sync across all your computers - it's like having "Exchange lite" behind the scenes.
If you did not want to pay a continuing subscription fee (for Office 365) then you might want to investigate getting a 3rd party add-in that would do the synchronization for you. There are many listed here:
http://www.howto-outlook.com/tag/sync
Mike Sperry
http://www.SperrySoftware.com
Find 37 Outlook add-ins that can make a difference!