We present 3D smoothed particle hydrodynamics simulations of protoplanetary discs undergoing a flyby by a stellar perturber on a parabolic orbit lying in a plane inclined relative to the disc mid-plane. We model the disc as a mixture of gas and dust, with grains ranging from 1 μm to 10 cm in size. Exploring different orbital inclinations, periastron distances, and mass ratios, we investigate the disc dynamical response during and after the flyby. We find that flybys induce evolving spiral structure in both gas and dust that can persist for thousands of years after periastron. Gas and dust structures induced by the flyby differ because of drag-induced effects on the dust grains. Variations in the accretion rate by up to an order of magnitude occur over a time-scale of the order of 10 yr or less, inducing FU Orionis-like outbursts. The remnant discs are truncated and warped. The dust disc is left more compact than the gas disc, both because of disc truncation and accelerated radial drift of grains induced by the flyby.