I'm currently using a secondary 24" monitor (widescreen) in portrait mode (rotated 90 degrees to be vertical). Is there a way to have the default Mac OS wallpaper adjust to maintain the image resolution quality?
Those pictures are located in
Meaning not in your user's library folder but the one at the root of the Mac hard drive.
I would Option-drag the ones you like out onto the desktop and then put them in your Pictures folder. Then you will have to rotate them manually in a graphic editing app (Preview.app will do this).
Rotate them the direction you want to by 90 degrees and then save them back to where you copied them to.
You should now be able to select a "portrait mode" Apple-default desktop picture. I imagine some will look odd on their side but then they were designed for landscape mode.
You might be better served searching for portrait desktop pictures on your favorite search engine as you will find a lot out there, probably at least some of which you might like a lot.