In this paper, we analyze joint channel, carrier frequency offset (CFO), and phase noise estimation in orthogonal frequency division multiplexing (OFDM) relaying networks. To achieve this goal, a detailed transmission framework involving both training and data symbols is first presented. Next, a novel algorithm that applies the training symbols to jointly estimate the channel responses, CFO, and phase noise parameters based on the maximum a posteriori criterion is proposed. Additionally, to evaluate the performance of the proposed channel estimation and carrier recovery algorithms, we analyze the ambiguities among the estimated parameters. Based on this analysis, a new Hybrid Cramér-Rao Lower Bound (HCRLB) is derived, which can effectively avoid such ambiguities. The simulation results show that the proposed estimation algorithm can achieve a performance close to the derived HCRLB.