This paper proposes a solid-state-LiDAR-inertial-visual fusion framework containing two subsystems: the solid-state-LiDAR-inertial odometry (SSLIO) subsystem and the visual-inertial odometry (VIO) subsystem. Our SSLIO subsystem has two novelties that enable it to handle drastic acceleration and angular velocity changes: (1) the quadratic motion model is adopted in the in-frame motion compensation step of the LiDAR feature points, and (2) the system has a weight function for each residual term to ensure consistency in geometry and reflectivity. The VIO subsystem renders the global map in addition to further optimizing the state output by the SSLIO. To save computing resources, we calibrate our VIO subsystem’s extrinsic parameter indirectly in advance, instead of using real-time estimation. We test the SSLIO subsystem using publicly available datasets and a steep ramp experiment, and show that our SSLIO exhibits better performance than the state-of-the-art LiDAR-inertial SLAM algorithm Point-LIO in terms of coping with strong vibrations transmitted to the sensors due to the violent motion of the crawler robot. Furthermore, we present several outdoor field experiments evaluating our framework. The results show that our proposed multi-sensor fusion framework can achieve good robustness, localization and mapping accuracy, as well as strong real-time performance.