You should do a Restore using iTunes
Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support
but if that's not possible with the iPod in its current condition (because it does not appear in iTunes), when you run Disk Utility on the Mac, does the iPod appear in the Disk Utility sidebar? If it does (and you cannot do a Restore using iTunes), you can try doing an Erase using Disk Utility to reformat it. But it needs to be done in a particular way. It says in your profile info that you use Mac OS X 10.7.5 (Lion). Is that still current info? I ask, because the current OS X (El Capitan) has a re-designed Disk Utility that works differently.