Odometry based on Inertial, Dynamic and Kinematic data (IDK-Odometry) for autonomous cars has been widely used to compute the prior estimation of Bayesian localization systems which fuse other sensors such as camera, RADAR or LIDAR. IDK-Odometry also gives the vehicle information by way of emergency when other methods are not available. In this work, we propose the use of deep neural networks to estimate the relative pose of the car given two timestamps of inertial-dynamic-kinematic data. We show that a neural network can find a solution to the optimization problem employing an approximation of the Vehicle Slip Angle (VSA). We compared our results to an IDK-Odometry system based on an Unscented Kalman Filter and Ackermann-wheel odometry. To train and test the network, we used a dataset which consists of ten driven trajectories with our autonomous car. Moreover, we successfully improved the results of the network employing collected data with a model autonomous car in order to increase the trajectories with high VSA.