How to handle this irregular opening.

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Mirigeganto

After move 6 in an uncommon opening I found myself with strong central control and a bishop pair.  However, none of the subsequent positions look too attractive.  I've run the position through Rybka and I don't quite like those resulting positions either.  I suppose what I am trying to ask is:  How can white nurture an advantage after black's sixth move?  Also, forgive me if the diagram is messed up, this is my first time making one.

The rest of the game was not too interesting as he kept dropping pawns and I was winning until I hung my queen under time pressure.

Splane

I think your 7th and 8th moves were good ones. His knight on d4 is his best piece and your bishop on f3 is a bad piece due to the pawn structure, so you don't mind if he plays 8. ...N:f3.

I think your 9th move is a positional blunder.

You have the two bishops so you should be looking to open up the position with 9. dc6 Nc6 10. Nc3 when his position is full of holes, you have a massive space advantage, and his pieces are all bad. 

after that one plan for you would be to castle kingside and advance the queenside pawns to open lines for your rooks.

Another idea would be to play Bg4, Be6 and Bd5 when the bishop dominates the board.

Your failure to take en passant also means his knight can never be dislodged from its fine outpost on d4.