The parallel propulsion system is the primary choice for power systems of large-scale ships. However, its operational state is influenced by multiple parameters, and unclear dynamic mechanisms critically restrict its navigation stability and reliability. This study develops a coupled lateral-torsional-longitudinal nonlinear dynamic model to establish the mapping between the key system parameters and the transmission vibration amplitude as well as the gear meshing state. Through the global sensitivity analysis, this study investigates the main effect sensitivity, total effect sensitivity, and interaction effect sensitivity of different parameters on the transmission structure, identifying the dominant factors affecting meshing vibration for different gear pairs. Subsequently, both full-scale ship vibration tests and small-scale prototype experiments are conducted to thoroughly investigate the influence patterns of various parameters on the vibration, acoustic, and power efficiency characteristics of the system. The research results provide essential technical support for a reasonable parameter configuration in such systems and for proactively mitigating the risk of abnormal vibrations.