Oh man. What I do know is that it's a hypermodern approach, and that usually I've seen black commit to such a strategy.
I think it'd be easier if you presented an official line that looks this way, then we can analyse the reasoning behind it. That'll be easier to work with.
But, generally, the idea is to put both your bishops on e6 and d6, castle, and then put your queen on d7 to connect the rooks.
As for white, I think they might play e3, next, to both develop the knight and prepare for a center battle. Unless of course white wants to coax black into overextending the center pawns, then they might develop the knights to f3 and c3.
Of course white loses his opening advantage playing like that but he develops his pieces logically and doesn't have any weakness so you shouldn't expect a huge advantage. Personally I would just occupy the center and develop normally e.g. d5 e5 Nc6 (maybe f5) Nf6 Bd6 0-0 and take it from there. As you said his space disadvantage makes it hard to find squares for his knights.
Well, my name is not Harry, but I'll also take that advice. That's just beautiful. Usually as a beginner I would've been slightly reluctant to castle long, but after studying the Sozin attack a bit, as well as the Richter Rauzer, my strategy was refreshed.
Thanks for all the advice. Lots of helpful ideas.
if they start with g3 I recommend a very offbeat response. a5!. The Lasker Simul Special! Using your queen and bishop you can push that pawn as far as a3 and cramp up their kingside.
This is a very crude example, but it works well I have found.
TBH it seems to me something like this would claim the center, and be less likely to fall victim to some strange pet line.
With ideas of Nc6, Be7 maybe, and 0-0. If 5. c4 then I like 5...Nc6 (though computer recommends d4), and if cxd5 then exd5 and you are already equal with open lines.
Though for my personal repertoire, I'll often play something like:
With ideas of Old Indian or King's Indian.
A finachetto development helps keep your c, d, and e files unblocked. For example a bishop on d3 blocks the d file. On e2 it blocks the e file. etc.
A finchetto bishop tends to dislike a knight on the 3rd rank (for white) or 6th rank (for black) because it blocks the bishop. Usually this knight repositions itself or develops to the 2nd rank straight away in the opening. An f3 knight often goes to h4 or d2 for example.
But a finchetto bishop doesn't mind a knight in the center. So while the N@f3 might annoy the B@g2, a knight on e4 doesn't 
. Basically this is because a centralized knight is strong.
Another tip:
Players who are post-beginners, but still lack experience, sometimes rush to trade off their opponent's finachettoed bishop. For example vs a bishop on g7 they might play Be3 Qd2 and Bh6. This is not always good because sometimes the fianchettoed bishop is inactive. In some KID, KIA, and Pirc games you can get structures like this:
And then the other tricky sort of consideration is that whenever you trade bishops of the same color... you have to consider that maybe the player with weakened squares is you!
Honestly I didn't know whether to post this in the openings section or beginners section. For some reason at this rating its very popular for a player to fianchetto both of their bishops of the bat. So basically it looks like this:
Usually I end up playing something like this:
This kind of opening just doesn't look sound to me honestly. It seems white always ends up with a bad bishop, it's always awkward to develop the knights and as the game progresses the pawn structure just collapses. I'm looking for advice against it both from white and black perspective.