Robust multisensor fusion of multi-modal measurements such as IMUs, wheel encoders, cameras, LiDARs, and GPS holds great potential due to its innate ability to improve resilience to sensor failures and measurement outliers, thereby enabling robust autonomy. To the best of our knowledge, this work is among the first to develop a consistent tightly-coupled Multisensor-aided Inertial Navigation System (MINS) that is capable of fusing the most common navigation sensors in an efficient filtering framework, by addressing the particular challenges of computational complexity, sensor asynchronicity, and intra-sensor calibration. In particular, we propose a consistent high-order on-manifold interpolation scheme to enable efficient asynchronous sensor fusion and state management strategy (i.e. dynamic cloning). The proposed dynamic cloning leverages motion-induced information to adaptively select interpolation orders to control computational complexity while minimizing trajectory representation errors. We perform online intrinsic and extrinsic (spatiotemporal) calibration of all onboard sensors to compensate for poor prior calibration and/or degraded calibration varying over time. Additionally, we develop an initialization method with only proprioceptive measurements of IMU and wheel encoders, instead of exteroceptive sensors, which is shown to be less affected by the environment and more robust in highly dynamic scenarios. We extensively validate the proposed MINS in simulations and large-scale challenging real-world datasets, outperforming the existing state-of-the-art methods, in terms of localization accuracy, consistency, and computation efficiency. We have also open-sourced our algorithm, simulator, and evaluation toolbox for the benefit of the community: https://github.com/rpng/mins.