Recent advancements in LiDAR-Inertial Odometry (LIO) have boosted a large amount of applications. However, traditional LIO systems tend to focus more on localization rather than mapping, with maps consisting mostly of sparse geometric elements, which is not ideal for downstream tasks. Recent emerging neural field technology has great potential in dense mapping, but pure LiDAR mapping is difficult to work on high-dynamic vehicles. To mitigate this challenge, we present a new solution that tightly couples geometric kinematics with neural fields to enhance simultaneous state estimation and dense mapping capabilities. We propose both semi-coupled and tightly coupled Kinematic-Neural LIO (KN-LIO) systems that leverage online SDF decoding and iterated error-state Kalman filtering to fuse laser and inertial data. Our KN-LIO minimizes information loss and improves accuracy in state estimation, while also accommodating asynchronous multi-LiDAR inputs. Evaluations on diverse high-dynamic datasets demonstrate that our KN-LIO achieves performance on par with or superior to existing state-of-the-art solutions in pose estimation and offers improved dense mapping accuracy over pure LiDAR-based methods. The relevant code and datasets will be made available at https://**.