The stability of oblique detonation waves (ODWs) is a fundamental problem, and resistance of ODWs against disturbances is crucial for oblique detonation engines in high-speed propulsion. In this work, numerical studies on ODW stability in disturbed flows are conducted using the two-dimensional reactive Euler equations with a two-step induction-reaction kinetic model. Two kinds of flow disturbances are, respectively, introduced into the steady flow field to assess ODW stability, including upstream transient high-pressure disturbance (UTHD) and downstream jet flow disturbance (DJFD) with different durations. Generally, an ODW is susceptible to disturbances at larger wedge angles and stable at smaller wedge angles. In the unstable wedge angle range, different ODW structures and transition patterns are obtained after disturbances, including different locations of the primary triple points, different numbers of the steady triple points on the wave surface, and different transition patterns from the leading oblique shock wave to the ODW. It is found that the primary triple point tends to move upstream for the disturbances that can form a local strong detached bow shock wave near the wedge tip. In contrast, the wave surface and the transition pattern are susceptible to all of the disturbances introduced in this study. Despite the unstable responses of the ODWs to the disturbances, the ODWs can keep standing stability after disturbances, which is beneficial to the propulsion application of ODWs.