Unable to reinstall Mac OSX without an Apple ID that I don't know
You can put up to macOS 10.11 Yosemite on that Mac. 

If you have Macs at work see if you can download a copy of it there or from a friend. I have also heard that an Apple genius can help with that at an Apple Store as macOS is free toinstall on any Mac. 

Once you have downloaded the OS create a bootable USB key. DiskmakerX will make one for you, there is also a terminal command that you can use to do the same thing.

If you boot from installable media and then wipe the drive before proceeding with the installation that problem with an AppleID will go away and you will be free to register the OS under your own AppleID