This paper investigates pilot-aided channel estimation for two-way relay networks (TWRNs) in the presence of synchronization errors between the two sources. The unpredictable synchronization error leads to time domain offset and signal arriving order (SAO) ambiguity when two signals sent from two sources are superimposed at the relay. A two-step channel estimation algorithm is first proposed, in which the linear minimum mean-square-error (LMMSE) estimator is used to obtain initial channel estimates based on pilot symbols and a linear minimum error probability (LMEP) estimator is then developed to update these estimates. Optimal training sequences and power allocation at the relay are designed to further improve the performance for LMMSE based initial channel estimation. To tackle the SAO ambiguity problem, the generalized likelihood ratio testing (GLRT) method is applied and an upper bound on the SAO detection error probability is derived. By using the SAO information, a scaled LMEP estimation algorithm is proposed to compensate the performance degradation caused by SAO detection error. Simulation results show that the proposed estimation algorithms can effectively mitigate the negative effects caused by asynchronous transmissions in TWRNs, thus significantly outperforming the existing channel estimation algorithms.