A novel learning-optimization-combined 4D radar odometry model, named DNOI-4DRO, is proposed in this paper. The proposed model seamlessly integrates traditional geometric optimization with end-to-end neural network training, leveraging an innovative differentiable neural-optimization iteration operator. In this framework, point-wise motion flow is first estimated using a neural network, followed by the construction of a cost function based on the relationship between point motion and pose in 3D space. The radar pose is then refined using Gauss-Newton updates. Additionally, we design a dual-stream 4D radar backbone that integrates multi-scale geometric features and clustering-based class-aware features to enhance the representation of sparse 4D radar point clouds. Extensive experiments on the VoD and Snail-Radar datasets demonstrate the superior performance of our model, which outperforms recent classical and learning-based approaches. Notably, our method even achieves results comparable to A-LOAM with mapping optimization using LiDAR point clouds as input. Our models and code will be publicly released.