Understanding ego-motion and surrounding vehicle state is essential to enable automated driving and advanced driving assistance technologies. Typical approaches to solve this problem use fusion of multiple sensors such as LiDAR, camera, and radar to recognize surrounding vehicle state, including position, velocity, and orientation. Such sensing modalities are overly complex and costly for production of personal use vehicles. In this paper, we propose a novel machine learning method to estimate ego-motion and surrounding vehicle state using a single monocular camera. Our approach is based on a combination of three deep neural networks to estimate the 3D vehicle bounding box, depth, and optical flow from a sequence of images. The main contribution of this paper is a new framework and algorithm that integrates these three networks in order to estimate the ego-motion and surrounding vehicle state. To realize more accurate 3D position estimation, we address ground plane correction in real-time. The efficacy of the proposed method is demonstrated through experimental evaluations that compare our results to ground truth data available from other sensors including Can-Bus and LiDAR.