Visual degradation caused by limited visibility, insufficient lighting, and feature scarcity in underwater environments presents significant challenges to visual-inertial simultaneous localization and mapping (SLAM) systems. To address these challenges, this paper proposes a graph-based visual-inertial-acoustic-depth SLAM system that integrates a stereo camera, an inertial measurement unit (IMU), the Doppler velocity log (DVL), and a pressure sensor. The key innovation lies in the tight integration of four distinct sensor modalities to ensure reliable operation, even under degraded visual conditions. To mitigate DVL drift and improve measurement efficiency, we propose a novel velocity-bias-based DVL preintegration strategy. At the frontend, hybrid tracking strategies and acoustic-inertial-depth joint optimization enhance system stability. Additionally, multi-source hybrid residuals are incorporated into a graph optimization framework. Extensive quantitative and qualitative analyses of the proposed system are conducted in both simulated and real-world underwater scenarios. The results demonstrate that our approach outperforms current state-of-the-art stereo visual-inertial SLAM systems in both stability and localization accuracy, exhibiting exceptional robustness, particularly in visually challenging environments.