Short answer Norton Ghost claims to work with some USB enclosures, I haven't been able to get it work with mine.
Acronis True image does a backup while windows is running so it will work with any external device when backing up.
Restoring your system with Acronis would require access to the enclosure outside of Windows. I have no idea whether it supports all/noe/most/some/ external devices.
Here is a trick
I bought a 5 1/4 USB 2.0 enclosure ($35) then mounted a removeable 5 1/4 hard drive bay into that ($12 each).
I have compatible removeable bays in all my computers and so do a few of my friends. Of course you have to shutdown before removing a HD form a PC, but you can move the drives from system to system without a screwdriver, and you can access the drive via USB without restarting.
Wish I knew more.
If anyone has managed to get their USB enclosure recognized by Ghost or True Image please let me know.