In this paper, we study energy efficient orthogonal frequency division multiplexing (OFDM) relay system, where two source nodes communicate with each other via a half-duplex amplify-and-forward relay node. We aim to maximize the energy efficiency (EE), where both the transmit and circuit power consumptions are taken into consideration. To this end, we optimize the active number of subcarriers and the number of bits to each subcarrier at the two source nodes. The optimal solution turns out to be a bidirectional water-filling bit allocation to minimize the overall transmit power, and a subcarrier reduction algorithm to balance the transmit and circuit power consumptions. When the data amounts at the two source nodes are unequal, the bidirectional water-filling leads to a hybrid one- and two-way relaying strategy, which employs one-way relaying on some subcarriers and two-way relaying on some of the other subcarriers. Simulation results demonstrate that the hybrid one- and two-way relaying with subcarrier reduction, which is optimized towards EE, is more energy efficient than that without subcarrier reduction, which only minimizes the transmit power.