When you say you tried to connect it up to an external USB hard drive enclosure did you just mean by using cables or you literally took the drive out of the Iomega and put it in the USB enclosure? The latter is likely to let you access the data.
I don't know anything about the Iomega network hardware, but if it has a built-in server than it's possible (probable?) that the drive uses a Unix file system.
Try downloading one of the "LiveCD" versions of Linux (such as Fedora or Ubuntu), burn it to a DVD and boot from it with the drive connected to your PC. If you can see the data on the drive then you should be able to copy it to another FAT- or NTFS-formatted drive that Windows will be able to deal with.
I took the drive out of my USB enclosure and replaced it with the drive from the NAS enclosure.
After doing this and then pluggin the drive into my computer, the found new hardware bubble pops up but no drive is visible in My Computer.
Is your drive setup as a master? I had the same problem when I hooked an IDE hard drive to a USB to IDE/Sata adapter. I had to set the drive as a master and then it showed up in My Computer. I just laid the drive on my desk and it worked good. It will show up as a hard drive in My Computer.
I do not know anything about the Iomega network drive either.
Windows should show the drive in Disk Management but it won't assign a drive letter and make it visible in Windows Explorer unless it's got a Windows-compatible file system (which basically means FAT or NTFS).
It doesn't look hopeful. The fact that it's showing you partition info suggests that the drive is at least functioning at some minimal level, and may in fact be perfectly OK. But the fact that the partitions are unknown even in Fedora means that there's no way to access the data in them (at least not that I'm aware of...). My first guess would be that the IOmega unit is using some sort of proprietary scheme.
But I'm not a data recovery expert - I rely on backups and have never had to actually recover a drive so I'm really not familiar with what tools are available.
Are there any IOmega forums around? Some folks more familiar with the hardware may be able to suggest something.