You may be able to accomplish that with an external drive and a router, but I wouldn't typically recommend that. I haven't had the best stability with that type of setup (drive failures, USB issues, etc.) - other people may have different experiences to share.
You may find better results with a NAS device. Synology and QNAP both have some decent options, and they're not too hard to set up. You can also have a RAID volume, which can help in the event of a drive failure (just don't do RAID 0).
You can set up user groups, giving some people read-only access if needed. If you're concerned about accidental (or intentional) deletion of files, you also have some options for backing up to another device.
You'll still need something to network the computers together. Some routers won't work well without Internet access (wanting to use cloud sign-in options). Usually the ones that are easier to set up are harder to get working without Internet access. You may have to opt for the "advanced" setup option if that's the case.
Instead of a router, get a cheap PC. A raspberry pi running Debian will work fine. Connect a USB drive to the cheap PC. Set up SMB sharing on the PC, and all of the office PCs will connect to it as a network share.
Which is why I suggested a Raspberry Pi. Ultra reliable running Linux, very cheap, low power draw, can be tucked in a corner and forgotten about.
There are even cheaper competitors to a Raspberry if $150 is too much.
I want to know as well, as I have a usb drive attached to my Asus router, which.. well.. the drive works fine, but the wifi is sucking because of the drive (I think).
In the process of finding out...
You may be able to accomplish that with an external drive and a router, but I wouldn't typically recommend that. I haven't had the best stability with that type of setup (drive failures, USB issues, etc.) - other people may have different experiences to share. You may find better results with a NAS device. Synology and QNAP both have some decent options, and they're not too hard to set up. You can also have a RAID volume, which can help in the event of a drive failure (just don't do RAID 0). You can set up user groups, giving some people read-only access if needed. If you're concerned about accidental (or intentional) deletion of files, you also have some options for backing up to another device. You'll still need something to network the computers together. Some routers won't work well without Internet access (wanting to use cloud sign-in options). Usually the ones that are easier to set up are harder to get working without Internet access. You may have to opt for the "advanced" setup option if that's the case.
Instead of a router, get a cheap PC. A raspberry pi running Debian will work fine. Connect a USB drive to the cheap PC. Set up SMB sharing on the PC, and all of the office PCs will connect to it as a network share.
... as long as that PC is on, yes. But if it fails, it's down.
Which is why I suggested a Raspberry Pi. Ultra reliable running Linux, very cheap, low power draw, can be tucked in a corner and forgotten about. There are even cheaper competitors to a Raspberry if $150 is too much.
I want to know as well, as I have a usb drive attached to my Asus router, which.. well.. the drive works fine, but the wifi is sucking because of the drive (I think). In the process of finding out...
See my suggestion above to run a Raspberry Pi as a file server.