This study delves into the effect of stratified fluid on the stationary characteristics of oblique detonation within a confined combustor, with the objective of providing a reference for the advancement of oblique detonation engines. Oblique detonation engines possess remarkable advantages such as high thermal cycle efficiency and are highly suitable for high-Mach-number flight. However, ensuring the stationary of detonation waves remains a formidable challenge. In this research, two-dimensional Euler equations augmented by a two-step kinetic model are employed to conduct numerical analyses. The study reveals that in both unconfined and confined combustors, the oblique detonation wave exhibits distinct basic structures. Stratified gas with varying widths exerts a profound impact on the stationary of the oblique detonation wave, giving rise to diverse reflection structures, including the regular reflection mode, Mach reflection mode, and the novel mode where the Mach stem is connected to a normal detonation wave. The formation mechanism of these complex structures is investigated, with particular emphasis on the crucial role of the triple-wave point. The presence of an inert gas layer within the stratified fluid configuration not only alters the Mach number behind the shock/detonation wave but also modifies the angles of the reflected shock wave in both the inert gas layer and the combustible gas layer. These changes lead to a series of unique interactions that ultimately govern the behavior of the oblique detonation wave.