Chemical diversity among metal-poor stars in the old stellar components in the Milky Way (MW), namely the thick disk and stellar halo, provides clues to understanding the early chemodynamical evolution of our Galaxy. We present our results on a homogeneous chemical abundance analysis for nearby metal-poor stars likely belonging to the MW thick disk, inner and outer stellar halos. Abundances of alpha, sodium, iron-peak and neutron-capture elements in the sample stars have been estimated using high-resolution (R 50000) spectra obtained with the High Dispersion Spectrograph mounted on the Subaru Telescope. The derived abundances are used to examine differences and similarities in elemental abundance ratios among the kinematically defined thick disk, inner and outer halo subsamples in the metallicity range of −3.3 < [Fe/H] < −0.5. We show that, in the metallicity range of [Fe/H] < −2, the three subsamples are similar in most of the elemental abundances. On the other hand, in the higher metallicities, particularly in [Fe/H] > −1.5, the thick disk and the inner/outer halo subsamples show systematically different abundance ratios for some elements including alpha, sodium, zinc and europium. A modest difference in the sodium and zinc abundances between the inner- and outer halo subsamples is also identified. The observed distinct abundances of some elements among the three subsamples implies that their constituent stars originally formed in progenitor systems that have experienced different star formation and chemical enrichment histories.