The extended use of laser welding in the industry requires a less sensitive process in terms of geometrical tolerances of the joint edges. As the industrial availability of laser systems increases, the demand to use laser welding technology possibly with parts coming from less precise production steps is increasing. Gap formation is often caused by the edge quality of the parts coming from previous manufacturing steps such as sheet forming. Al alloy sheets deformed to box-shaped 3D forms often require welded joints on the edges in lap, but, and corner joint configurations. These joints are hard to carry out by laser welding due to the large gap formation caused by the tolerances of the deformation processes involved. Laser welding of Al alloys is already challenging in the absence of gap formation, while these joint configurations have been not feasible with a stationary beam due to incomplete fusion and defect formation. Laser welding with beam oscillation and wire feeding can improve the weldability of these joints. The oscillating motion of the high-intensity beam can achieve a deep weld together with a wider seam. Combined with wire feeding, the process can close gaps in the butt, lap, and corner joint configurations. On the other hand, the added oscillation and wire-related parameters require extending the experimental space, which requires a methodological study to identify feasible conditions. Accordingly, this work proposes a methodological approach to identify and set laser welding process parameters with beam oscillation and wire feeding for an EN AW 5083. Process parameters were initially studied using a simple analytical model that depicts the beam trajectory. Bead-on-plate tests were conducted to assess beam size, power, and weld speed ranges. Lap, butt, and corner joint conditions with a 0.5-mm gap were welded with high quality by manipulating the laser power, oscillation amplitude, and wire feed rate. The results show that welding speeds could be maintained as high as 55 mm/s with complete filling of gaps of up to 0.5 mm, eliminating the surface undercuts and achieving weld widths in the order of 2.5 mm. Moreover the results show the possibility control the depth of the welds from 3 mm to full-penetration conditions.