In this work, we prepare transformable HEA/Cu nanolaminates (NLs) with equal individual layer thickness (h) by the magnetron sputtering technique, i.e., Fe50Mn30Co10Cr10/Cu and Fe50Mn30Co10Ni10/Cu, and comparatively study He-ion irradiation effects on their microstructure and mechanical properties. It appears that the as-deposited HEA/Cu NLs manifest two size h-dependent hardness regimes (i.e., increased hardness at small h and hardness plateau at large h), while the He-implanted ones exhibit monotonically increased hardness. Contrary to the fashion that smaller h renders less irradiation hardening in bimetal NLs, the Fe50Mn30Co10Cr10/Cu NLs manifest the trend that smaller h leads to greater irradiation hardening. By contrast, the Fe50Mn30Co10Ni10/Cu NLs exhibit the maximum irradiation hardening at a critical h = 50 nm. Below this critical size, smaller h results in lower radiation hardening (similar to bimetal NLs), while above this size, smaller h results in greater radiation hardening (similar to Fe50Mn30Co10Cr10/Cu NLs). Moreover, these transformable HEA/Cu NLs display inverse h-dependent strain rate sensitivity (SRS m) before and after He-ion irradiation. Nevertheless, compared with as-deposited samples, the irradiated Fe50Mn30Co10Cr10/Cu NLs display reduced SRS, while the irradiated Fe50Mn30Co10Ni10/Cu NLs display enhanced SRS. Such unusual size-dependent irradiation strengthening and inverse h effect on SRS in irradiated samples were rationalized by considering the blocking effects of He bubbles on dislocation nucleation and motion, i.e., dislocations shearing or bypassing He bubbles.