Unorthodox Openings

I am a lower rated player, so I meet a lot of Unorthodox Openings.  How would you recommend dealing with that? Should I continue with opening theory, or should I try something else? 

Don't continue with opening theory. Wait, that doesn't even make sense. How can you continue playing the theory if the game is already no longer within the theory? Anyway, don't do that. I'll go further, don't even start by trying to play theory to begin with. Opening principles is where it's at. Understanding the moves you're playing is far more important than playing the best move. You'll learn faster and you'll not have any problem in situations like the one mentioned in your OP. You probably won't even know when it is or isnt happening...

https://www.chess.com/article/view/the-principles-of-the-opening

There are two ways to meet them:

1. Try to play normal, logical developing moves. They might not be too challenging but usually you get a good position.

2. You can try to identify the weaknesses of those unorthodox moves in order to "refute" them.

#1 is the safer option...

You could buy "Taming Wild Chess Openings" or two other books:

"Taming Wild Chess Openings" is available as part of an ios app called e+chess which was developed in part by Jeremy silman.  It allows you to buy many chess books then play out the moves on your ipad or iphone.  "Taming Wild Chess Openings" is there for $11.99.

http://www.amazon.com/Beating-Unusual-Chess-Openings-Annoying/dp/1857444299/ref=sr_1_2?s=books&ie=UTF8&qid=1464270361&sr=1-2&keywords=unorthodox+openings+chess

http://www.amazon.com/Unorthodox-Openings-Publishings-Essential-Repertoire/dp/1580420729/ref=sr_1_3?s=books&ie=UTF8&qid=1464270448&sr=1-3&keywords=unorthodox+openings+chess

or http://www.amazon.com/Taming-Wild-Chess-Openings-Board/dp/9056915703/ref=sr_1_1?s=books&ie=UTF8&qid=1464270544&sr=1-1&keywords=taming+wild+chess

You could learn unorthodox replies to unorthodox openings, thus turning the tables on your opponent.  For instance in an OTB game about 30 years ago against a USCF expert who opened with 1.b4?! I replied 1...c6, and a few moves later he missed his best 4th move

4.c4! is not an obvious tactic, I would not expect someone to find that over the board unless they had actually studied the theory of 1.b4.  More likely your opponent was just trying to clown you, or didn't want to expose their actual preparation.

Well it's something that an expert-rated 1.b4 player should know, unless it was completely a lark and he figured he could beat me with anything since he was rated 400-500 points higher than me.

Opening Theory? On Unorthodox openings?? Never heard of it. Just kidding. Work on your opening understanding, not opening theory. Basically in the opening you need to complete three tasks:

1.Develop the pieces (Knights before bishops)

2.Castle

3.Connect the rooks (moving the queen)

Play your pawn to e8 and take his king. 

Chess is a funny old game, mainly because of how people perceive it and the way it should be played.

I think any answer to your question should be predicated on first find out what sort of chess you play. For instant if you are playing a lot of bullet slash blitz then the answers given by C-Crusher & Jenium have merit.

On the other hand if you are playing a lot of standard (or even turn based internet correspondence) then their answers still have merit but will only get you so far if you do not understand what you are doing and what you want to achieve.

As much as the "Tin Foil Hat Brigade" would like you to believe chess is not as simple as plugging moves into chess software and then prostrating oneself with absolute faith at the altar of its evaluations. The two biggest questions you have to ask yourself when confronted with a "snake oil" opening is "Why?" and "What?"...for example WHY has this been played and WHAT does it achieve. Question everything.

Opening principle and general theories are fine but without an ideas and plans to apply them, I can NOT see you achieving much

Crippled Apple- I had a look at your post and your rating.  2 pieces of advice.

1 Don't spend too much of your time on opening theory until you get stronger, much stronger.  Spend your time on strategy, tactics, endings... And when you do come to study openings don't just memorise moves, learn from some source that will tell you the ideas behind the openings and look at model games.

2 When confronted by odd openings fall back on sound development and central control.  Playing eccentric openings means that they are normally not really the best moves, and what theory there is may be less reliable, so you have a bit of margin for error [well, hopefully].  

Long ago I played a lot against a strong player who like 1b4 for white.  As a result I know quite a bit of theory, and a lot of players who like 1b4 don't.  It always amuses me when "caught" in their eccentric opening and I am better by move 4.