In this paper, the performance of two-way multiuser mixed radio frequency/free space optical (RF/FSO) relay networks with opportunistic user scheduling and asymmetric channel fading is studied. RF links are used to conduct data transmission between users and relay node, while a FSO link is used to conduct data transmission on the last-mile communication link between the relay node and base station. The RF links are assumed to follow a Rayleigh fading model, while the FSO links are assumed to follow a unified Gamma-Gamma atmospheric turbulence fading model with pointing error. First, closed-form expressions for the exact outage probability, asymptotic (high signal-to-noise ratio) outage probability, average symbol error rate, and average ergodic channel capacity are derived assuming a heterodyne detection scheme. The asymptotic results are used to conduct a power optimization algorithm where expressions for optimal transmission power values for the transmitting nodes are provided. Additionally, performance comparisons between the considered two-way-relaying (TWR) network and the oneway- relaying (OWR) network are provided and discussed. Also, the impact of several system parameters, including number of users, pointing errors, atmospheric turbulence conditions, and outage probability threshold on the overall network performance are investigated. All the theoretical results are validated by Monte Carlo simulations. The results show that the TWR scheme almost doubles the network ergodic capacity compared to that of the OWR scheme with the same outage performance. Additionally, it is shown that under weak-to-moderate weather turbulence conditions and small pointing error, the outage probability is dominated by the RF downlink with a neglected effect for the user selection process at the RF uplink transmission. However, for severe pointing error, the outage probability is dominated by the FSO uplink/downlink transmission.