Position for analysis - Black to move

OK, I had this position OTB, black (me) to move.  Not sure when I started seeing these kind of moves, but my eyes were immediately drawn to 1.  ..Qxd4!, which I played without really looking at all continuations (I did, of course, see the knight fork following 2. Qxd4).

My opponent responded with 2. Bxe6+ , and the game continued Bxe6 3. O-O-O Nxa2+ 4. Nxa2 Qxd2+ 5. Qxd2 Bxa2 6. b3, trapping the a2 bishop, but ultimately giving me a net 3 pawns once that bishop was traded for the b3 pawn.

Looking at it, it's hard to say if 2. Qxd4 Nxc2+ followed by 3. Nxd4 is better or worse than this, I was fairly well convinced that 2. Nxe6 was worse due to Qxe5+.  Whenever I play a combo like this, I want to know (1) whether it is sound, and (2) what the best defense against it would have been. 

2.Bxe6+ throws away a piece for no reason, so it's a confusing variation you give.

As for your question. 2.Qxd4 Nxc2+ is definitely better for white than throwing away a piece.

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To find the best defense (or at least, the best one you're able to find, none of us are computers) calculate each line, render an evaluation in your mind for the end position (not necessarily a number, but who you think is better and why) then, finally, compare the two evaluations. That's basically what analysis is.

Other than counting material in most positions I usually put an emphasis on minor pieces. Whose are better. Of course there are other things like king safety, who controls an open file, etc, but almost always it's worth it to imagine the end position in your mind, and carefully look at the minor pieces too.

So here's what I did

Looking back, I see you can think of it in terms of giving up the d and e pawns or the d and c pawns.

Giving up e5 unleashes the bishop, but giving up c2 means white thinks he can keep e5 defended and not lose a 3rd pawn (which seems unlikely in the long run). Giving up e5 right away lets white's rooks have access to e6. So in an OTB game, I'd probably start thinking the 3rd example is white's best try.

Thanks for the detailed analysis!  I hadn't considered 1. ..Bb3 at all, and I agree that this looks best of the options presented.  The other lines look about where I saw them.

The clubs I play in have more creative attackers than precise defenders (myself included in the former category), so I often find myself launching into these sorts of combinations.

 I'm happy if someone / you find it useful

Yeah, I didn't notice Bb3 either. I was only planning on doing two diagrams, then I noticed afterwards.

That's why I think it's important to pause and think of candidates. I love blitz, I play it a lot, and calculation rarely stops in the middle. It's straight from the first move to the end, so to speak, but in tournament play you have time to pause after move 1, 2, 3, etc, and look around.

Yeah, but that kind of passivity doesn't compare to 1. ..Qxd4 in terms of effect.

Now that I look at it, 2. O-O-O seemed promising at first, but after 2. ..Qxe5 3. R(d or h)e8 Nxa2+looks really dangerous for white.