<p>The odd controllable spatiotemporal Airy Ince-Gaussian (CAIG) beam and the even controllable spatiotemporal CAIG beam is investigated theoretically and numerically by solving the (3 + 1)D Schrödinger equation in cylindric coordinates. Typical examples of the obtained solutions are based on the ratio of the input power and the critical power, the direction factor, the ellipticity and mode number in strongly nonlocal nonlinear media (SNNM). The properties of the two spatiotemporal Airy Ince-Gaussian beams, which is combined by the odd CAIGs beam and the even CAIG beams, propagating collinearly in SNNM are studied. The controllable spatiotemporal Airy hollow Ince-Gaussian (CAhIG) wave packets are attained in SNNM. The CAhIG wave packets will keep approximately non-dispersion properties in temporal dimension. If the ratio of the input power and the critical power isn’t equal to 1, the CAhIG beams periodically oscillating during propagation. The direction of the energy flow of CAhIG wave packets in spatial domain will rotate clockwise or counterclockwise around the propagating center. The energy flow density distribution of vortices can be applied to the noninvasive capture of particles. Their Poynting vector snapshots at different propagating distances are shown.</p>