Channel tracking in millimeter wave (mmWave) vehicular systems is crucial for maintaining robust vehicle-to-infrastructure (V2I) communication links, which can be leveraged to achieve high accuracy vehicle position and orientation tracking as a byproduct of communication. While prior work tends to simplify the system model by omitting critical system factors such as clock offsets, filtering effects, antenna array orientation offsets, and channel estimation errors, we address the challenges of a practical mmWave multiple-input multiple-output (MIMO) communication system between a single base station (BS) and a vehicle while tracking the vehicle's position and orientation (PO) considering realistic driving behaviors. We first develop a channel tracking algorithm based on multidimensional orthogonal matching pursuit (MOMP) with factoring (F-MOMP) to reduce computational complexity and enable high-resolution channel estimates during the tracking stage, suitable for PO estimation. Then, we develop a network called VO-ChAT (Vehicle Orientation-Channel Attention for orientation Tracking), which processes the channel estimate sequence for orientation prediction. Afterward, a weighted least squares (WLS) problem that exploits the channel geometry is formulated to create an initial estimate of the vehicle's 2D position. A second network named VP-ChAT (Vehicle Position-Channel Attention for position Tracking) refines the geometric position estimate. VP-ChAT is a Transformer inspired network processing the historical channel and position estimates to provide the correction for the initial geometric position estimate. The proposed solution is evaluated using raytracing generated channels in an urban canyon environment. For 80% of the cases it achieves a 2D position tracking accuracy of 26 cm while orientation errors are kept below 0.5 degree.