<p>Accurate representation of environmental geometry is critical for LiDAR-based SLAM systems. Although 3D Gaussian models efficiently encode local structures through covariance matrices, their fixed-scale parameterization often fails to maintain geometric fidelity in complex and uncertain environments. To address this, we propose MGM-LIO, a novel LiDAR-Inertial Odometry (LIO) system that integrates a multiscale Gaussian model within an Invariant Extended Kalman Filtering (InEKF) framework. MGM-LIO introduces the fast Gaussian filter (FGF), a preprocessing module that directly extracts multiscale Gaussian parameters from raw point clouds, eliminating the need for traditional downsampling. This approach preserves geometric fidelity while significantly reducing data size. Furthermore, we introduce a novel normal visibility criterion (NVC) during multiscale Gaussian association and updating, effectively filtering unreliable matches caused by viewpoint occlusion and ambiguous surface normals, especially at large scales. Additionally, we employ a sparse hashed voxel map embedding a binary-tree structure to generate coarse-to-fine Gaussian parameters, enabling efficient distribution-to-distribution registration. By integrating IMU data using the InEKF framework, MGM-LIO achieves robust and efficient state estimation. Extensive evaluations on publicly available and self-collected datasets demonstrate that MGM-LIO achieves higher accuracy and computational efficiency on par with or superior to state-of-the-art methods.</p>