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Multi-sensor fusion of multi-modal measurements from commodity inertial, visual and LiDAR sensors to provide robust and accurate 6DOF pose estimation holds great potential in robotics and beyond. In this paper, building upon our prior work (i.e., LIC-Fusion), we develop a sliding-window filter based LiDAR-Inertial-Camera odometry with online spatiotemporal calibration (i.e., LIC-Fusion 2.0), which introduces a novel sliding-window plane-feature tracking for efficiently processing 3D LiDAR point clouds. In particular, after motion compensation for LiDAR points by leveraging IMU data, low-curvature planar points are extracted and tracked across the sliding window. A novel outlier rejection criterion is proposed in the plane-feature tracking for high-quality data association. Only the tracked planar points belonging to the same plane will be used for plane initialization, which makes the plane extraction efficient and robust. Moreover, we perform the observability analysis for the LiDAR-IMU subsystem and report the degenerate cases for spatiotemporal calibration using plane features. While the estimation consistency and identified degenerate motions are validated in Monte-Carlo simulations, different real-world experiments are also conducted to show that the proposed LIC-Fusion 2.0 outperforms its predecessor and other state-of-the-art methods.