The idea behind opening theory is that it is such because, besides showing what to do in opening situations, it also show what not to do; namely this means that a good way to practice opening theory is to take one line and purposely move a figure otherwise, so that you understand how to punish it (for example try the standard Spanish opening without the book and see how White/Black can capture this or that other pawn if played otherwise). This helps on the long run to understand in general how to punish moves that are out of book (if they were sound they would then be in the book, somewhere).
Coming to the actual question we see few different points:
How does one wanting to stick to principles deal with such unorthodox play?
this depends very much on what you mean by "unorthodox play": if unorthodox means, say,
1.e4 b6 2. d4 Bb7 3.Nc3 e6
that is not really unorthodox, rather it follows a different principle of occupancy of the centre via indirect control; it is sound and it is indeed in the books, just not on Chapter 1. As a consequence either you just play following natural development or, if you wish, you can go deeper into those lines and learn their theory. If, otherwise, your opponent plays manifestly wrong moves, blundering pawn protections and the like, well, you just take that pawn on, say d5, left as a gift.
I struggle against players who follow no opening and just bring out the queen and run amuck on the board.
Well, if the Queen is running wild on the board then just developing the two Knights in their proper squares (f3-c3 vs f6-c6) will definitely make your opponent spend many tempi, resulting in their pieces not being developed. As a consequence you will then have major figures development and initiative; this, obviously, unless the Queen is there for a good reason (see for example all the lines containing the "poised pawn" on b2-b7 or the old-style King's gambits and Cambridge Springs variations).
Am I just too new to understand that there are book responses to such moves or should I focus on repulsing pieces before I develop or should I just follow my plan for development?
I would say it is half-half: improvement in chess follows the path of both ideas/principles and book analysis. Continue doing what you are doing and the improvements and the results will come as the time goes by.