How can I tell from viewing my Library which photos are in which albums?

You can create a Smart Album. Open the Photos app on a Mac, then File menu > New Smart Album and set the condition to Album - is not - Any for example and that smart album will display photos that are not in any album.

If you want to know which album a photo is in, add a keyword with the name of the album to the photo. You can do this easily by opening each album in turn selecting all photos in the album with ⌘A, then opening the Info and writing the name of the album into the keywords field.