What is Black's best move in this position? [Title "Black to move"]
[StartFlipped "0"]
[fen "r1b1kb2/pp1p2pp/2n1qn2/3P4/3p4/2N4P/PPP2PP1/R1BQR1K1 b q - 0 1"]


What is Black's best move in this position? 

Would black's best move be Qxe1?
[FEN "r1b1kb2/pp1p2pp/2n1qn2/3P4/3p4/2N4P/PPP2PP1/R1BQR1K1 b KQkq - 1 1"]

1... Qxe1+ 2.Qxe1+ Ne7 (2... Kd8 3.dxc6 dxc3) 3.d6 dxc3 4.dxe7 Bxe7


Yes, Black's "best" move is Qxe1+. His queen is pinned against his king, so it will be lost on the next move whatever happens. Black may as well get as much material back for the queen as possible, which means taking the rook.  But then Black is down queen for two minor pieces, with his king stuck in the centre and bad development: he should just resign.

The real question is not "What should I do if I get into this position?" but "How should I avoid getting into this position in the first place?"