We report a systematic magnetotransport study on high-crystallinity overdoped (LSNO) thin films with x = 0.20-0.24. By conducting pulsed-field transport experiment up to 62 T, we reveal two salient features of the normal-state transport in this LSNO thin films: (1) the magnetoresistivity does not follow the Kohler's scaling rule but exhibit a H-linear behavior in the high H/T limit and (2) the normal-state resistivity below 30 K consistently follows a behavior across the overdoped regime. Our results demonstrate a coexistence of strange-metal and Fermi-liquid transport features in the unconventional superconductor and provide new information on the transport characteristics of the normal ground state that host superconductivity in infinite-layer nickelates.