If I plug in four separate Dual Strike USB gamepads to my computer then will the Dual Strike software realize there are four separate gamepads connected and allow me to configure each one separate than the other?
First of all, I don't have dual strikes, but have heard 2 or three are okay, but sometimes if a forth is plugged in, it's slower than the rest. Mind you, this is only what I heard.
When you plug game controllers into a USB port (any of the 127 available ports allowed) then how does the software remember the mapping for the gamepad located in USB port 5 and keep those settings different than the gamepad in USB port 3 say?
Depends on the driver.

I think USB port # only matters at bootup when checking against last shutdown. I don't think it matters once the device is unplugged and replugged.
Some drivers remember the individual serial number (like a license plate #) of the device, others just remember the device ID (like a car model & make). If the dual strike drivers are like the first, you can unplug and replug as you want. If it's the latter, you need to plug them in in the same order they were installed and only when the computer is on, or have a max of one unplugged at a time and maybe do the plugging/unplugging only when the computer is on.
Also, I guess the Dual Strike software somehow lets you map individual keystrokes to each of the buttons/triggers
Yes, but unless you want to use those buttons outside of mame, I advise not doing this. Mame can map a joystick buttons to things like UI_Cancel (usually ESC) without the driver remapping to a keystroke. Having the driver do the remapping will slow down the joystick response speed a little, and if the driver does a lot of remapping, it really slows it down. And if you need to have the driver remap, it's better to have one joystick with 2 buttons remapped, than two joysticks each with one button remapped.