Ok, I'm gonna give my 2 cents, I'm probably totally wrong...

I would play Nxd2

The outpost on e4 is nice, but a simple capture by white leaves a pawn there, not a piece. White has a potential outpost on e5, and you cant really capture there, because it will leave white with a passed pawn. So, Nxe2, to prevent Nf3-e5.

My thoughts exactly. In the game I played Nxc3, but realized that it was bad about a second later.

EDIT:

I'm sure you know this, but it's vital that Black has the possibility of carrying out a frontal attack on e3, so that's the main reason why White can't be allowed to exchange on e4 and force the Knight to be replaced by a pawn.

I don't think it's that simple a question, but I have to go along with Nxd2. My follow-up would involve Nf6, Qe7, and Rae1, clamping down on e4 and pressuring the backward pawn on e3.. I think the position would favor Black somewhat, but I'm not sure exactly how he would continue

I haven't even thought about that, but you're right, of course.

I'd say Black has a big advantage. That's how I continued I think. I would post the rest of the game, but unfortunately I wrote down a lot of the moves completely wrong and can't remember exactly how I continued after that. What happened was after tying some of his pieces down to the defense of e3 he then allowed me to create a second weakness on a2 and eventually win a pawn which I didn't manage to convert in the Endgame due to my general lack of technique and he managed to get a draw.

EDIT: As I've said I didn't continue with Nxd2, but with Nxc3, but luckily he didn't play the maneuver Nf3-e5.

1.Blacks knight is well placed

2.Black has gud space advantage

3.Blacks white bishop can gt diagonal by playing Ba6

I think it's placed OK at the moment on b7. It can always go to a6 a little later if required.

I agree with most comments. Nxd2 hinders the ability for white to occupy an outpost, and that backward e pawn gives black a safe advantage, so you don't want that file closed off.