We propose a real-time dynamic LiDAR odometry pipeline for mobile robots in Urban Search and Rescue (USAR) scenarios. Existing approaches to dynamic object detection often rely on pretrained learned networks or computationally expensive volumetric maps. To enhance efficiency on computationally limited robots, we reuse data between the odometry and detection module. Utilizing a range image segmentation technique and a novel residual-based heuristic, our method distinguishes dynamic from static objects before integrating them into the point cloud map. The approach demonstrates robust object tracking and improved map accuracy in environments with numerous dynamic objects. Even highly non-rigid objects, such as running humans, are accurately detected at point level without prior downsampling of the point cloud and hence, without loss of information. Evaluation on simulated and real-world data validates its computational efficiency. Compared to a state-of-the-art volumetric method, our approach shows comparable detection performance at a fraction of the processing time, adding only 14 ms to the odometry module for dynamic object detection and tracking. The implementation and a new real-world dataset are available as open-source for further research.