Parallel bridges subjected to aerodynamic interference can experience wake-induced vibrations (WIVs) within the wind speed range allowed for vehicle operation, affecting ride comfort, and running safety. Wind tunnel tests are conducted to obtain vertical and torsional WIV responses of the leeward railway bridge, and aerodynamic coefficients for both the bridge and the suburban railway vehicle. Displacement-based and harmonic wake-induced force models are developed, and a novel WIV–WVB (Wind–Vehicle–Bridge system considering WIV responses) analysis model is proposed. The analysis focuses on the effects of factors such as buffeting forces, WIV mode orders, bridge entry time, and WIV amplitude on running performance. Results show that the vertical and torsional WIV responses are reproduced using both wake-induced force models align well with test results. At higher wind speeds, the difference in vehicle dynamic responses with and without buffeting forces becomes pronounced. Vertical WIV significantly elevates the vertical acceleration (up to 59.1%) and offload factor (up to 42.9%), while lateral vehicle dynamic responses remain largely unaffected. Higher mode orders further amplify the increases in vertical acceleration and offload factor, and these responses become more sensitive to changes in vehicle speed. Torsional WIV elevates all vehicle dynamic responses, particularly increasing vertical and lateral accelerations by 53.5% and 30.2%, respectively. At constant torsional WIV amplitude levels, vehicle responses exhibit greater sensitivity to changes in vehicle speed and are less influenced by wind speed variations. Vertical acceleration is highly sensitive to changes in vertical and torsional WIV amplitude and is the first to exceed the limit as amplitude increases.