Robust and accurate navigation is critical for Unmanned Aerial Vehicles (UAVs) especially for those with stringent Size, Weight, and Power (SWaP) constraints. However, most state-of-the-art (SOTA) LiDAR-Inertial Odometry (LIO) systems still suffer from estimation inconsistency and computational bottlenecks when deployed on such platforms. To address these issues, this paper proposes a consistent and efficient tightly-coupled LIO framework tailored for UAVs. Within the efficient Multi-State Constraint Kalman Filter (MSCKF) framework, we build coplanar constraints inferred from planar features observed across a sliding window. By applying null-space projection to sliding-window coplanar constraints, we eliminate the direct dependency on feature parameters in the state vector, thereby mitigating overconfidence and improving consistency. More importantly, to further boost the efficiency, we introduce a parallel voxel-based data association and a novel compact cluster-to-plane measurement model. This compact measurement model losslessly reduces observation dimensionality and significantly accelerating the update process. Extensive evaluations demonstrate that our method outperforms most state-of-the-art (SOTA) approaches by providing a superior balance of consistency and efficiency. It exhibits improved robustness in degenerate scenarios, achieves the lowest memory usage via its map-free nature, and runs in real-time on resource-constrained embedded platforms (e.g., NVIDIA Jetson TX2).