Unfortunately, none of the Microsoft Windows operating systems support installation on USB or FireWire external devices. With that said, it may be possible to install Windows 7 on an eSATA external drive as Windows 7 typically recognizes eSATA drives as internally connected.
However, please keep in mind that when you install Windows 7 or any operating system, typically speaking, the operating system installs with the connected hardware in mind. In other words, installing Windows 7 on an external drive and then physically installing the formerly external hard drive to a different computer with a different configuration is not recommended. For more information you may benefit from the following TechNet forum thread Can I install Windows 7 onto an external USB hard drive?
The question begs to be asked, why not just physically install the hard drive in question to the computer in question as a primary hard drive? It sounds as though you may be attempting to create images / imaged hard drives and then proceed to install them in the necessary machines. There are a plethora of other Microsoft utilities that may be more beneficial to you with this aforementioned scenario. A good place to start would be to check out the following