Event-based cameras are bio-inspired sensors with pixels that independently and asynchronously respond to brightness changes at microsecond resolution, offering the potential to handle state estimation tasks involving motion blur and high dynamic range (HDR) illumination conditions. However, the versatility of event-based visual odometry (VO) relying on handcrafted data association (either direct or indirect methods) is still unreliable, especially in field robot applications under low-light HDR conditions, where the dynamic range can be enormous and the signal-to-noise ratio is spatially-and-temporally varying. Leveraging deep neural networks offers new possibilities for overcoming these challenges. In this paper, we propose a learning-based stereo event visual odometry. Building upon Deep Event Visual Odometry (DEVO), our system (called Stereo-DEVO) introduces a novel and efficient static-stereo association strategy for sparse depth estimation with almost no additional computational burden. By integrating it into a tightly coupled bundle adjustment (BA) optimization scheme, and benefiting from the recurrent network's ability to perform accurate optical flow estimation through voxel-based event representations to establish reliable patch associations, our system achieves high-precision pose estimation in metric scale. In contrast to the offline performance of DEVO, our system can process event data of \zs{Video Graphics Array} (VGA) resolution in real time. Extensive evaluations on multiple public real-world datasets and self-collected data justify our system's versatility, demonstrating superior performance compared to state-of-the-art event-based VO methods. More importantly, our system achieves stable pose estimation even in large-scale nighttime HDR scenarios.