We present results from Subaru Fiber Multi Object Spectrograph near-infrared spectroscopy of 118 star-forming galaxies at z∼1.5 in the Subaru Deep Field. These galaxies are selected as [O ii]λ3727 emitters at z ≈ 1.47 and 1.62 from narrow-band imaging. We detect the Hα emission line in 115 galaxies, the [O iii]λ5007 emission line in 45 galaxies, and Hβ, [N ii]λ6584, and [S ii]λλ6716, 6731 in 13, 16, and 6 galaxies, respectively. Including the [O ii] emission line, we use the six strong nebular emission lines in the individual and composite rest-frame optical spectra to investigate the physical conditions of the interstellar medium in star-forming galaxies at z∼1.5. We find a tight correlation between Hα and [O ii], which suggests that [O ii] can be a good star formation rate indicator for galaxies at z∼1.5. The line ratios of Hα/[O ii] are consistent with those of local galaxies. We also find that [O ii] emitters have strong [O iii] emission lines. The [O iii]/[O ii] ratios are larger than normal star-forming galaxies in the local universe, suggesting a higher ionization parameter. Less massive galaxies have larger [O iii]/[O ii] ratios. With evidence that the electron density is consistent with local galaxies, the high ionization of galaxies at high redshifts may be attributed to a harder radiation field by a young stellar population and/or an increase in the number of ionizing photons from each massive star.