Accurate localization is essential for the safe and effective navigation of autonomous vehicles, and Simultaneous Localization and Mapping (SLAM) is a cornerstone technology in this context. However, The performance of the SLAM system can deteriorate under challenging conditions such as low light, adverse weather, or obstructions due to sensor degradation. We present A2DO, a novel end-to-end multi-sensor fusion odometry system that enhances robustness in these scenarios through deep neural networks. A2DO integrates LiDAR and visual data, employing a multilayer, multi-scale feature encoding module augmented by an attention mechanism to mitigate sensor degradation dynamically. The system is pretrained extensively on simulated datasets covering a broad range of degradation scenarios and fine-tuned on a curated set of real-world data, ensuring robust adaptation to complex scenarios. Our experiments demonstrate that A2DO maintains superior localization accuracy and robustness across various degradation conditions, showcasing its potential for practical implementation in autonomous vehicle systems.