Connect the drive to one of the HP ENVYs. This machine will have to be on when other machines connect to the drive.
Right click a folder on the external drive that you want to share and select Properties. On the Sharing tab press the Advanced Sharing button. Check the Share this folder button. Call the Share what you want it to be called, add comments if you would like. Set permissions. Each user will have to have an account and password set up on this machine. Change means they can delete and write, Read means read only. No one needs full control.
After you have set up the Share you need to set up the Security. Change to the Security tab. Press the Edit button. Add the users you added for Share access and grant them the same rights you want them to have to the Share. Modify and below for users who can delete and create, Read & execute and below for those that are read only. Again, no one needs full control.
Once you have the share set up the easiest way to connect it is to create a batch file on the other machine. The contents of the file will be similar to this.
NET USE S: /D
NET USE S: \\COMPUTER\SHARE /USER:NAME PASSWORD
Where S: is the drive letter, COMPUTER is the name of the computer sharing the drive, SHARE is the name of the share, NAME is the name of the account you want to access the share, and PASSWORD is the password of the account NAME. Create the file in Notepad and save with a .BAT file extension.
For the Galaxy, I would use Dropbox or a similar service. For the PCs you can store the files on the external drive and then use Dropbox to sync them to the cloud for the Galaxy to access.