Most of the existed works on the radio resource allocation (RRA) problem commonly assume the channel-state information (CSI) can be perfectly obtained by the transmission source. However, such assumption is not practical in the realistic wireless systems. In this work, we consider the practical implementation issues of resource allocation in orthogonal frequency division multiple access (OFDMA) two-way relay networks: the inaccuracy of channel-state information (CSI) available to the source. Instead, only the estimated channel status is known by the source. In this context, a joint optimization of subcarrier pairing and allocation, relay selection, and transmit power allocation is formulated in OFDMA two-way amplify-and-forward relay networks. Moreover, the objective of this work is to minimize the energy consumption of the overall system. Further, to ensure the quality of service (QoS) or data rate 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 with guaranteeing the required data rates. Through simulation studies, energy consumption performance of the systems under the proposed schemes is investigated. It can be observed that our proposed scheme can improve the energy consumption performance of the considered system.