Oblique impact of droplet onto a deep liquid pool is frequently observed in nature. As for engineering applications, the subsequent phenomenon of oblique droplet impact is of great significance for a proper design of the vanes in the extreme ultraviolet (EUV) chamber of ASML to prevent contamination. During the impact, the pool surface deforms and a cavity is generated, which later on collapses into a jet that shoots upward. Meanwhile, a liquid crown will be visible above the surface. When this crown becomes unstable, splashing occurs. We study these phenomena numerically by using fully three dimensional simulation in Basilisk C, an open source CFD package, coupled with an adaptive Cartesian grid and volume-of-fluid (VOF) method. The simulation is validated by both qualitative and quantitative comparison with the available experimental results and theory. In both simulation and experiment, three types of impact phenomena are identified: smooth coalescence of droplet with the pool, splashing in the impact direction only, and splashing in all directions. We quantify these three regimes by accounting for the Weber number and the droplet impingement angle, and compare the results with the experimental data and scaling argument proposed in the previous literature. We also study cavity dynamics and shape. The growth of the cavity angle is captured by our simulation. In analogy to the perpendicular drop impact, we give a model for the cavity expansion, from which we obtain a temporal function for the cavity depth which is in agreement with the simulation. The magnitude of the cavity depth and the displacement match with the available experimental data. Besides, our simulation captures the scaling dependence of both the depth and the displacement on the Weber number. We further point out the connection between the descent of the crown and the initiation the cavity collapse. The three-dimensional details about the crown behavior and cavity formation from our simulation provide an insight of the phenomena which could cause contamination in the EUV chamber, and offer an opportunity for a further research on this subject.