In this paper, we investigate the strong coupling effects between a meta-atom and a metal-insulator-metal (MIM) nanocavity. By changing the meta-atom sizes, we achieve the meta-atomic electric dipole, quadrupole or multipole interaction with the plasmonic nanocavity, in which characteristic anticrossing behaviors demonstrate the occurrence of the strong coupling. The various interactions present obviously different splitting values and behaviors of dependence on the meta-atomic position. The largest Rabi-type splittings, about 360.0 meV and 306.1 meV, have been obtained for electric dipole and quadrupole interaction, respectively. We attribute the large splitting to the highly-confined cavity mode and the large transition dipole of the meta-atom. Also the Rabi-type oscillation in time domain is given