This paper investigates a channel-coded multiuser system operated with orthogonal frequency-division multiplexing (OFDM) and interleaved division multiple-access (IDMA). To realize the potential advantage of OFDM-IDMA, two challenges must be addressed. The first challenge is the estimation of multiple channel parameters. An issue is how to contain the estimation errors of the channel parameters of the multiple users, considering that the overall estimation errors may increase with the number of users because the estimations of their channel parameters are intertwined with each other. The second challenge is that the transmitters of the multiple users may be driven by different RF oscillators. The associated frequency asynchrony may cause multiple CFOs at the receiver. Compared with a single-user receiver where the single CFO can be compensated away, a particular difficulty for a multiuser receiver is that it is not possible to compensate for all the multiple CFOs simultaneously. To tackle the two challenges, we put forth a framework to solve the problems of multiuser channel-parameter estimation, CFO compensation, and channel decoding jointly and iteratively. The framework employs the space alternating generalized expectation-maximization (SAGE) algortihm to decompose the multisuser problem into multiple single-user problems, and the expectation-conditional maximization (ECM) algorithm to tackle each of the single-user subproblems. Iterative executions of SAGE and ECM in the framework allow the two aforementioned challenges to be tackled in an optimal manner. Simulations and real experiments based on software-defined radio indicate that, compared with other approaches, our approach can achieve significant performance gains.