Grant-free non-orthogonal multiple access (NOMA) is promising to achieve low latency massive access in Internet of Things (IoT) applications. In grant-free NOMA, pilot signals are often used for user activity detection (UAD) and channel estimation (CE) prior to multiuser detection (MUD) of active users. However, the pilot overhead makes the communications inefficient for IoT devices with sporadic transmissions and short data packets, or when the channel coherence time is short. Hence, it is desirable to improve the efficiency by avoiding the use of pilot signals, which can also further achieve lower latency. This work focuses on Bayesian receiver design for grant-free low density signature orthogonal frequency division multiplexing (LDS-OFDM), where each user is allocated a unique low density spreading sequence. We show how to achieve joint UAD, CE and MUD without the use of pilot signals. Firstly, the task of joint UAD, CE and MUD is formulated as a novel structured signal estimation problem. Then the structure of the effective channel matrix is encoded to a probabilistic form, and message passing based Bayesian approach is developed to solve the structured signal estimation problem. In particular, belief propagation (BP), expectation propagation (EP) and mean field (MF) message passing are used to develop efficient hybrid message passing algorithms to achieve trade-off between performance and complexity. Simulation results demonstrate the effectiveness of the proposed receiver for grant-free LDS-OFDM without the use of pilot signals.