The PSE software is available to be installed and run on a computer (no other types of devices such as tablets).
You get the installer file either by download (only solution from Adobe directly) or on a DVD (from big Web resellers).
The license is for a single user.
The installer, download or DVD can install the software itself on any number of computers.
To be able to run a given computer, you have to 'activate' the link with the licensing server from the menu Help >> sign in. You are allowed to 'activate' two computers, typically a desktop and a laptop at the same time, but you should not use them at the same time (single user license)
If you have already activated two computers and want to activate a third one, you have to deactivate (menu Help >> Sign out) one of the already activated computers.
So, the answer is that you can have your four computers with the program installed with your downloaded or DVD installer.
You can have two of those activated at the same time.
You can switch the activation for two computers in the same location.
But you are not allowed to use or let other users use two activated computers at the same time.
Sharing of your media and catalogs:
You can backup and restore your catalogs and media from the organizer, which allows keeping copies on various computers as well as allowing to migrate your data and organization from one computer to a new one.
In your case (just like me), I would store the catalog AND media files on an external drive which I can plug in to any activated computer without having to do anything else.