<<What I want to do is make an image of my laptop's disk in such a way that (after changing the BIOS settings to boot from USB) I can boot from this external drive on any other capable computer, and it is as if I am working on my original computer (less whatever hardware changes there might be) but I would be on any other given computer capable of booting off of a USB.>>Some Google Links to Explore.
A major flaw in thought, as I perceive it.
A USB or any other drive...is only a storage medium.
Any clone/backup of the system...still needs the system...or it's of no value unless one just wants an assortment of files.
The system is the hardware, operating system...and software working together. Eliminate any one of those and you have something that is less than a system.
What I would suggest...rather than backup, clone the current hard drive to a larger (if that's the key) laptop hard drive
...which could then be inserted into the laptop as a replacement...anytime.