I've never heard this term, but I can give it a try.
Most Western musical pieces are built around a certain set of notes known as a scale. For example, the "C" scale consists of the notes C,D,E,F,G,A,B--that is, the white keys of a piano. To oversimplify greatly, if you play a more or less random series of these notes, you will get a melody that is more or less pleasing, especially if you begin and end with the root (or "tonic") note of C.
If you start off with the C scale, and then begin introducing notes played on the black keys, such as C-sharp, G-flat, etc., you're going to get something much more exotic, and probably not very pleasing.
Perhaps that is what is meant by "strange" notes: notes that do not "belong" in the scale that is being used.
(Of course, if you know what you're doing, those "strange" notes can turn "Mary had a little lamb" into something with real spice.)
Not knowing the context in which strange notes is used, I must assume the author means notes which a student is not already aquainted with. We practice to gain knowledge of what we do not already know, so strange notes will no longer be strange to us! If that is too obvious, give me the context and I will try again. Another idea is the use of shape notes, or modern notation in ethereal sections. Some of that notation can be pretty strange.