To mitigate the inter-symbol interference (ISI), multiple access interference (MAI) and the effect of different Doppler shifts within a data package incurred in variably mobile asynchronous underwater multiuser communications (VMAUMC), a Kalman filter-based chip differential blind adaptive multiuser detection (D-KF-BAMUD) algorithm is proposed in this paper. The Kalman filter-based blind adaptive multiuser detection (KF-BAMUD) algorithm has been adopted to combat ISI and MAI in the scenario of static users, and underwater and under-ice multiuser communication experiments have been carried out to verify the effectiveness of the KF-BAMUD algorithm. To tackle the more challenging VMAUMC, a differential modulation and demodulation technique operating at the chip level is proposed to reduce the impact of Doppler shift residues after the Doppler compensation with an average Doppler frequency offset within each data package. The technique is combined with KF-BAMUD algorithm, leading to D-KF-BAMUD algorithm, which is able to effectively handle ISI, MAI and the effect of Doppler shift residues simultaneously in VMAUMC. This paper reports our experiments on VMAUMC carried out in Songhua River in April 2016 (7 users, data rate 7.87bit/s, up to 2m/s variably relative velocity in each data package, and horizontal distance 200m shallow-water channel between transducer and hydrophone), and the encouraging experimental results demonstrate the effectiveness of the proposed system and the D-KF-BAMUD algorithm.