In intelligent vehicle navigation, especially where GNSS signals are unavailable or unreliable, accurate and efficient sensor data processing is critical to maintain robust performance. Classical calibration methods for Inertial Measurement Units (IMUs), such as discrete and system-level calibration, fail to capture time-varying, nonlinear, and non-Gaussian noise characteristics. Likewise, Kalman filters typically assume static measurement noise levels for Non-Holonomic Constraints (NHC), resulting in suboptimal performance in dynamic environments. Furthermore, zero-velocity detection plays a vital role in preventing error accumulation by enabling reliable zero-velocity updates during motion stops, but classical thresholding approaches often lack robustness and precision. To address these limitations, we propose a novel multitask deep neural network (MTDNN) architecture that jointly learns IMU calibration, adaptive noise estimation for NHC, and zero-velocity detection solely from raw IMU data. This shared-encoder design improves generalization, reduces overfitting, and minimizes computational overhead, enabling real-time deployment on resource-constrained platforms such as Raspberry Pi. The model is trained using post-processed RTK/INS ground truth trajectories obtained from both a proprietary dataset and the publicly available KITTI and 4Seasons datasets. Experimental results confirm the proposed system's superior accuracy, efficiency, and real-time capability in GNSS-deprived conditions.