Impairments like time varying phase noise (PHN) and carrier frequency offset (CFO) result in loss of synchronization and poor performance of multi-relay communication systems. Joint estimation of these impairments is necessary in order to correctly decode the received signal at the destination. In this paper, we address spectrally-efficient multi-relay transmission scenarios where all the relays simultaneously communicate with the destination. We propose an iterative pilot-aided algorithm based on the expectation conditional maximization (ECM) for joint estimation of multipath channels, Wiener PHNs, and CFOs in decode-and-forward (DF) based multi-relay orthogonal frequency division multiplexing (OFDM) systems. Next, a new expression of the hybrid Cramér-Rao lower bound (HCRB) for the multi-parameter estimation problem is derived. Finally, an iterative receiver based on an extended Kalman filter (EKF) for joint data detection and PHN tracking is employed. Numerical results show that the proposed estimator outperforms existing algorithms and its mean square error performance is close to the derived HCRB at differnt signal-to-noise ratios (SNRs) for different PHN variances. In addition, the combined estimation algorithm and iterative receiver can significantly improve average bit-error rate (BER) performance compared to existing algorithms. In addition, the BER performance of the proposed system is close to the ideal case of perfect channel impulse responses (CIRs), PHNs and CFOs estimation.