There's great solutions out there for use on hosted machines. You could install a Lamp Server on a virtual machine on a computer that's always on, and run
Feng office. That would be your best option. You can also host a forum or what have you if that works better. This also keeps things internal, if that's what you're concerned about (as long as you don't allow your server access outside the network).
But alternately, you can setup a shared folder and sync the share to all workstations, but you run the risk of loosing edits, sync errors, and things like that.