In Chrome, I can shift+click to automatically select all tabs in between the tab I'm on and the tab I click on, and then press ctrl+W to close them. Is there any way I can achieve this with Firefox?
Unfortunately no, there is nothing like this for Firefox like there is for Chrome. (Well, there is, but it's so irritating that it's worthless.) Firefox has an add-on where you can customize the shortcut keys, but it doesn't allow you to add new ones. There is also an unofficial add-on extension that gives Firefox that same ability and with 18k votes @ 4/12 stars I say it works.
Here are the two links from Firefox that tell you all the shortcut keys. I personally still use the middle mouse scroll to kill tabs fast.