What do you do against center game?

How do you play against center game as black?

I respond 1.e4 with 1..., e5 But after 2. d4 I don't have a system that I like to play as black...

I'd like something aggressive or trappy. Any suggestions?

First of all you can go c5

For traps with black https://youtu.be/jzQKQ96FAng

This is the main theory against center game and this position looks prominent for both sides

Another main line is 4.Qe3 Nf6 5.Nc3 Bb4.

why don't you like Thriller's Fan's line? Black either wins a clean pawn on e4 or has very nice development and a good share of the center compared to White's

It is obligatory for Black to take on d4 as there is no good way to defend the e5 pawn. 

3.Qxd4 Nc6 4.Qa4 to my knowledge is pretty harmless and Black can just develop normally.

Similar things can be said for 4.Qe3.

If 3.c3, which is a pretty dangerous pawn sac if Black doesn't know about it, I recommend 3...d5! striking back in the center.

2...d6 3.Nf3 is known to yield clear advantage for White (if Black wants to play the Philidor he should opt for 1.e4 d6 2.d4 Nf6 3.Nc3 e5), and I am pretty sure Nimzowitsch is not the soundest opening either. 

In any case, why go for any of these when 2...exd4 is so much more natural and, frankly, better?

While i think you are heavily underestimating both the philidor and the e5 nimzowitsch, i cant argue against the fact  that exd4 is simply by far the best move in the center game.

Here for example, the pirc move order to reach the philidor is ONLY superior if black is committed to reaching the hanham variation of the philidor. IF black prefers the antonin variation or the larsen variation, he is better served with the normal order. Same if he really wants to avoid the queenless  endgame.