This work extends previous kinematic studies of young stars in the head of the Orion A cloud (OMC-1/2/3/4/5). It is based on large samples of infrared, optical, and X-ray selected pre-main-sequence stars with reliable radial velocities and Gaia-derived parallaxes and proper motions. Stellar kinematic groups are identified assuming they mimic the motion of their parental gas. Several groups are found to have peculiar kinematics: the NGC 1977 cluster and two stellar groups in the extended Orion nebula (EON) cavity are caught in the act of departing their birthplaces. The abnormal motion of NGC 1977 may have been caused by a global hierarchical cloud collapse, feedback by massive Ori OB1ab stars, supersonic turbulence, cloud-cloud collision, and/or slingshot effect; the former two models are favoured by us. EON groups might have inherited anomalous motions of their parental cloudlets due to small-scale 'rocket effects' from nearby OB stars. We also identify sparse stellar groups to the east and west of Orion A that are drifting from the central region, possibly a slowly expanding halo of the Orion nebula cluster. We confirm previously reported findings of varying line-of-sight distances to different parts of the cloud's Head with associated differences in gas velocity. 3D movies of star kinematics show contraction of the groups of stars in OMC-1 and global contraction of OMC-123 stars. Overall, the head of Orion A region exhibits complex motions consistent with theoretical models involving hierarchical gravitational collapse in (possibly turbulent) clouds with OB stellar feedback.