The present work extends Part I of our study to investigate the flow dynamics and scalar mixing of a turbulent gaseous jet in an oscillating crossflow. Attention is first given to intrinsic flow instabilities under a steady condition. Both power spectral density and proper orthogonal decomposition analyses are applied. For the case with a jet-to-crossflow velocity ratio of 4, the two most dynamic modes, corresponding to jet Strouhal numbers of around 0.1 and 0.7, are identified as being closely linked to the shear-layer vortices near the injector orifice and the vertical movement in the jet wake region, respectively. The effect of oscillation imposed externally in the upstream region of the crossflow is also examined systemically at a jet-to-crossflow velocity ratio of 4. A broad range of forcing frequencies and amplitudes are considered. Results reveal that the dominant structures observed in the case with a steady crossflow are suppressed by the harmonic excitations. Flapping–detaching motions, bearing the forcing frequencies and their subharmonics, become dominant as the forcing amplitude increases. The ensuing flow motions lead to the formation of a long, narrow jet plume and a relatively low mixing zone, which substantially alters the mixing efficiencies as compared to the case with a steady crossflow.