As others have noted, Obduction takes a long time to load using a conventional hard drive. If I purchased an external ssd would I be able to store the game on the ssd and thus drastically shorten the time to load it? If so, what size ssd should I purchase?

You can store the game wherever you like, if you use the offline installer. Galaxy may have specific requirements, that restrict placing games anywhere

Whether you "drastically" shorten loading times, is another matter, certainly using an external drive isn't usually the best option.

Depending on your hardware, that often means a USB connection, which defeats the entire point of using an SSD.
Newer MOBO's may have a dediicated external SSD port, but usually the best results are using an internal socket.

My SSD is SATA3 (6GB), and internally housed, Loading a new save from scratch can take about 20 seconds, whereas it's halved with reloads of same area. In game loading is not a big deal, with moving between words, hidden behind graphical effects, not seeming to bad.

Depending on what your SSD is running on, better speeds can be obtained than mine, which is 4 years old.
It's the connection used, that gives the boost, more than just being an SSD, an external USB connection is slowing the process to that speed, and not taking advantage of the SSD.

Better to move your HDD content to the SSD, and connect the HDD externally, using a USB housing if needed.
General rule is, if it 's a running proogram, it's on SSD, if it's stored, or run once, like installers it stays on the HDD.
Your OS will benefit from the SSD as well as the game, and that has a knock on effect on everything you run.