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We analyze the O VI content and kinematics for 126 H I-selected absorbers at 0.14 ≲ z ≲ 0.73 for which the metallicities of their cool photoionized phase have been determined. We separate the absorbers into 100 strong Lyα forest systems (SLFSs with 15 ≲ logN(H I) < 16.2) and 26 partial Lyman Limit systems (pLLSs with 16.2 ≤ log N(H I) ≤ 17.2). The sample is drawn from the COS CGM Compendium (CCC) and has O VI coverage in signal-to-noise ratio ≥ 8 Hubble Space Telescope/COS G130M/G160M QSO spectra, yielding a 2σ completeness level of $\mathrm{log}N$(O VI) ≥ 13.6. The O VI detection rates differ substantially between low-metallicity (LM; [X/H] ≤ -1.4) and high-metallicity (HM; [X/H] > -1.4) SLFSs, with 20% and 60% detection rates, respectively. The O VI detection frequency for the HM and LM pLLSs is, however, similar at ∼60%. The SLFSs and pLLSs without detected O VI are consistent with the absorbing gas being in a single phase, while those with O VI trace multiphase gas. We show that the O VI velocity widths and column densities have different distributions in LM and HM gas. We find a strong correlation between O VI column density and metallicity. The strongest ($\mathrm{log}N$(O VI) ≳ 14) and broadest O VI absorbers are nearly always associated with HM absorbers, while weaker O VI absorbers are found in both LM and HM absorbers. From comparisons with galaxy-selected and blind O VI surveys, we conclude absorbers with $\mathrm{log}N$(O VI) ≳ 14 most likely arise in the CGM of star-forming galaxies. Absorbers with weak O VI likely trace the extended CGM or intergalactic medium, while those without O VI likely originate in the intergalactic medium.