In this work, we consider the practical issues of resource allocation problem in OFDMA two-way relay networks: the inaccuracy of channel-state information (CSI) available to the transmitters. Instead, only the estimated channel status is known by the transmitters. In this context, a joint optimization of subcarrier pairing and allocation, relay selection and transmit power allocation is formulated in the OFDMA two-way amplify-and-forward relay networks. Moreover, to ensure the Quality of Service (QoS) requirement, the energy consumption must be minimized without compromising the QoS. Therefore, by applying convex optimization techniques, energy efficient algorithms are developed with the objective to minimize the total transmit power while guaranteeing the required data rates. Through simulation studies, energy consumption performance of the systems under the proposed schemes are investigated. It is shown that the proposed scheme can improve the energy consumption performance without scarifying the QoS.