there a a few different ways you could approach this ....
An organised manual synchronisation of the .PST files to a USB drive. With this you set up both outlook copies to look for it's data on a USB stick, and then you manually take the USB stick to the office and back home.
A similar method involves locating the .PST file at a location that can be accessed from both locations - the location would have to be accessible using an internet link that sows the location as a mapped local folder
Another way would be the use of a remote session from home to work or work to home to run a single copy of the out look PST