We propose a Bayesian framework for the problem of multi-user dectection in the context of an unknown and time-varying number of active users. In this paper, we combine orthogonal frequency-division multiplexing modulation with multi-antenna reception to mitigate both the asynchronism and frequency-selectivity of the wireless medium. We develop a method for user identity and data detection with joint channel parameter estimation, performed on a per-OFDM block basis to account for a highly dynamic random-access channel. Based on a factor graph approach, we derive an inference algorithm based on message-passing resulting in an iterative code-aided receiver. We show that a suitable Gaussian approximation leads to a complexity that increases only linearly with the maximum number of users. Computer simulations show that the proposed iterative receiver has a low probability of erroneous activity detection, while maintaining a high antenna diversity order for active users