This paper proposes a Unified Monocular-Stereo Visual-Inertial State Estimator (UMS-VINS) that combines monocular, stereo vision, and inertial measurements for vehicle localization in degenerated scenarios. UMS-VINS is a tightly coupled visual-inertial odometry (VIO), which requires a stereo camera and a low-cost inertial measurement unit (IMU). On the one hand, we introduce additional two-dimensional sub-pixel features from the left and/or right cameras. With monocular-stereo features, UMS-VINS can improve the positioning accuracy and robustness by enhancing the quality and quantity of features. On the other hand, a mode selection-based visual-inertial initialization strategy is designed to dynamically choose between stereo visual odometry or VIO according to the inertial motion state and initialization status, which can guarantee successful initialization. The performance on both new real-world and public datasets demonstrates its effectiveness in terms of localization accuracy, localization robustness, and environmental adaptability.