This study addresses the challenges of porosity defects and grain coarsening inherent to local dry underwater laser welding of 304 austenitic stainless steel, a material widely used in nuclear power and marine engineering. To mitigate these issues, laser beam oscillation was integrated with a double-layer gas-curtain drainage system to secure a stable local dry environment. The individual effects of six key process parameters, including laser power, welding speed, wire feed rate, defocusing distance, oscillation frequency, and oscillation amplitude, on weld penetration, dilution ratio, and porosity were systematically investigated. Orthogonal design and range analysis quantified the relative significance of each parameter on weld morphology and defect formation. The results demonstrate that oscillation amplitude exerts the primary control over weld penetration, followed by defocusing distance, whereas oscillation frequency shows the least influence. Similarly, oscillation amplitude dominates porosity suppression, with defocusing distance acting as a secondary factor. Microstructural analysis indicated that high-frequency beam oscillation homogenizes the spatial energy distribution and induces forced convection within the molten pool. It is inferred that this dynamic stirring breaks up continuous columnar dendrites, decreases the average grain size from 32.37 to 21.52 μm (a 33.5% reduction), and effectively reduces porosity. Overall, this work provides empirical process data and microstructural control that may serve as a reference for future underwater laser repair applications.