Orthogonal signal division multiplexing (OSDM) is an emerging method for Internet of Underwater Things (IoUT) networks. The impulsive noise, the carrier frequency offset (CFO), and the time-varying underwater acoustic channel decrease the performance of underwater acoustic OSDM communications. In this article, the orthogonal projection and distributed compressed sensing (DCS) methods are utilized to facilitate the CFO, impulsive noise, and channel estimation. First, the received signal is compensated by different tentative CFOS. Then an orthogonal projection matrix is constructed and projects the received signals into a specific subspace, where the channel portion is zero. Second, the received signals after projection are combined to improve impulsive estimation under the framework of DCS method. Finally, an first-order derivative of residual method is introduced to measure the amount of impulsive noise dynamically. The proposed methods adopt pilot vectors for estimating the CFO, the impulsive noise, and the channel, as a result, the bandwidth is improved significantly. Moreover, the proposed methods improve the impulsive noise estimation under and lower SNR and fewer number of pilot vectors. Both numerical simulation and sea trial data are used to evaluate the performance of our proposed methods, the experimental results demonstrate the effectiveness of our proposed methods.