Multiple distributed nodes in cooperative networks generally are subject to multiple carrier frequency offsets (MCFOs) and multiple timing offsets (MTOs), which result in time varying channels and erroneous decoding. This paper seeks to develop estimation and detection algorithms that enable cooperative communications for both decode-and-forward (DF) and amplify-and-forward (AF) relaying networks in the presence of MCFOs, MTOs, and unknown channel gains. A novel transceiver structure at the relays for achieving synchronization in AF-relaying networks is proposed. New exact closed-form expressions for the Cramér-Rao lower bounds (CRLBs) for the multi-parameter estimation problem are derived. Next, two iterative algorithms based on the expectation conditional maximization (ECM) and space-alternating generalized expectation-maximization (SAGE) algorithms are proposed for jointly estimating MCFOs, MTOs, and channel gains at the destination. Though the global convergence of the proposed ECM and SAGE estimators cannot be shown analytically, numerical simulations indicate that through appropriate initialization the proposed algorithms can estimate channel and synchronization impairments in a few iterations. Finally, a maximum likelihood (ML) decoder is devised for decoding the received signal at the destination in the presence of MCFOs and MTOs. Simulation results show that through the application of the proposed estimation and decoding methods, cooperative systems result in significant performance gains even in presence of impairments.