I have a question, it's not a huge issue atm, but I'm curious.

Let's say I had an external hard drive, and the SATA to USB adapter broke, so I took out the hard drive and made it a 500 GB internal hard drive, and installed a 64 bit Linux OS.

Now let's imagine that the hard drive, while it was an external was using an NTFS file system, and now that it's hosting a Linux OS it's formatted in ext4. Is there any Linux software that I could use to recover remnants of photos that were on the hard drive and didn't get backed up before I formatted it? I'm going to start doing my own google searches, but I thought I'd post this here in case any of you guys have experience/suggestions for situations like this.

The probability of recovery would depend on how much space was used by the photos, and how much space was used when installing the Linux setup.

You just have to try it---the standard tool is photorec: http://www.cgsecurity.org/wiki/PhotoRec

You need to have the drive mounted or connected such that it is not being used for the OS, and is not written to. Then you need enough space on **another** drive to store the recovered files.

You could probably still recover some files, you can try photorec like mentioned or:
http://foremost.sourceforge.net/

And remember to recover the data to a DIFFERENT HDD than the one you are recovering from otherwise you may overwrite files you could have recovered.