Recently, deep learning methods and multisensory fusion have been applied to address odometry challenges in unmanned ground vehicles (UGVs). In this paper, we propose an end-to-end visual-lidar-inertial odometry framework to enhance the accuracy of pose estimation. Grayscale images, 3D point clouds, and inertial data are used as inputs to overcome the limitations of a single sensor. Convolutional neural network (CNN) and recurrent neural network (RNN) are employed as encoders for different sensor modalities. In contrast to previous multisensory odometry methods, our framework introduces a novel attention-based fusion module that remaps feature vectors to adapt to various scenes. Evaluations on the Karlsruhe Institute of Technology and Toyota Technological Institute at Chicago (KITTI) odometry benchmark demonstrate the effectiveness of our framework.