Most existing studies on joint activity detection and channel estimation for grant-free massive random access (RA) systems assume perfect synchronization among all active users, which is hard to achieve in practice. Therefore, this paper considers asynchronous grant-free massive RA systems and develops novel algorithms for joint user activity detection, synchronization delay detection, and channel estimation. In particular, the framework of orthogonal approximate message passing (OAMP) is first utilized to deal with the non-independent and identically distributed (i.i.d.) pilot matrix in asynchronous grant-free massive RA systems, and an OAMP-based algorithm capable of leveraging the common sparsity among the received pilot signals from multiple base station antennas is developed. To reduce the computational complexity, a memory AMP (MAMP)based algorithm is further proposed that eliminates the matrix inversions in the OAMP-based algorithm. Simulation results demonstrate the effectiveness of the two proposed algorithms over the baseline methods. Besides, the MAMP-based algorithm reduces 37% of the computations while maintaining comparable detection/estimation accuracy, compared with the OAMP-based algorithm.