The practical implementation of Oblique Detonation Wave Engines (ODWEs) utilizing liquid hydrocarbon fuels is fundamentally constrained by the prolonged ignition delay and atomization dynamics inherent to high-speed two-phase flows. Previous studies have explored ignition initiation through detonator strips and jet-induced ignition on wedge surfaces [1, 2]. This study proposes and computationally validates the use of transverse liquid jets to facilitate the robust ignition and stabilization of oblique detonation waves (ODWs) within a confined combustor. Simulations are conducted using a supersonic reactive Eulerian-Lagrangian solver, developed within the OpenFOAM framework, coupling a skeletal n-heptane chemical mechanism with the PSI-CELL method. We identify three distinct wave topologies governed by the jet-inflow momentum ratio (J): the ODW-SSW (Separation Shock Wave) regime, the ODW-MS (Mach Stem)-SSW regime, and the ODW-MS regime. The analysis elucidates the critical role of the transverse jet in altering the shock structure and enhancing droplet residence time in the recirculation zone. Notably, the transverse jet configuration demonstrates exceptional stability under unsteady inflow conditions. Systematic investigations reveal that regimes with lower momentum ratios successfully sustain the detonation front even under inlet pressure oscillations with relative amplitudes of up to 50%. The flow field exhibits a hysteretic mode transition that effectively maintains the detonation wave within the combustor. These findings establish the transverse liquid jet not merely as an ignition trigger but as a viable stable detonation control method for ensuring the operational robustness of liquid-fueled ODWEs.