You really have a couple of questions here.
First, when it comes to memorization in chess, it has been shown that the more positions you have seen, the more likely you are to remember other positions. I remember once that GM Susan Polgar was given some random chess positions, and she remembered the "normal" ones exceptionally well, however, when the positions were more random, she remembered at a rate that was roughly what anyone else remembered them.
There are books, unrelated to chess, that deal with learning to memorize better. I would love to see Master Simon Reinhard, World Memory Champion, write a book on memorizing specifically aimed at chess memorization.
Here are a couple more articles specifically on memorization that you might find interesting.
Memory Techniques: the Peg system (Part One)
Memory Techniques: the Peg system (Part Two)
Memory Techniques: the chess equation
Your second question, "what are some good strategies to try to recognize a position and understand which opening it came from?", is more about applying any memorization techniques to learning opening pawn structures, and the plans that are associated with them.
There are many books on this from the very basic, "Chess Opening Essentials: The Complete Series" by New In Chess to the classic "Pawn Structure Chess" by GM Andy Soltis to the more advanced, and outstanding, "Chess Structures: A Grandmaster Guide" by GM Mauricio Flores Rios.
These types of books teach you what you are aiming for in the opening, in general, and thus, when your opponent does not play "book" moves, you are not just lost with no idea what to do. You just have to read these types of books, and absorb some of the positions, and then you are back to the experiment with GM Polgar, even if not on the same level. You will begin to memorize, and recognize more.