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Intergalactic absorbers along lines of sight to distant quasars are a powerful diagnostic for the evolution and content of the intergalactic medium (IGM). In this study, we use the Far Ultraviolet Spectroscopic Explorer (FUSE) satellite to search 129 known Lyα absorption systems at z<0.15 toward 31 active galactic nuclei (AGNs) for corresponding absorption from higher Lyman lines and the important metal ions O VI and C III. We detect O VI in 40 systems, over a smaller range of column density (logN_OVI_=13.0-14.35) than seen in H I (logN_HI_=13.0-16.0). The coexistence of O VI and H I suggests a multiphase IGM with warm photoionized and hot ionized components. With improved O VI detection statistics, we find a steep distribution in O VI column density, dN_OVI_/dNOVI_∝N-2.2±0.1^_OVI_, suggesting that numerous weak O VI absorbers contain baryonic mass comparable to the rare strong absorbers. Down to 30 mÅ equivalent width (O VI λ1032) we find an absorber frequency dN_OVI_/dz~17±3. The total cosmological mass fraction in this hot gas is at least Ω_WHIM=(0.0022±0.0003)[h₇₀(Z_O/0.1Z_☉)(f_OVI_/0.2)]^–1, where we have scaled to fiducial values of oxygen metallicity, O VI ionization fraction, and the Hubble constant. Gas in the warm-hot intergalactic medium (WHIM) at 10⁵-10⁶ K contributes at least 4.8%±0.9% of the total baryonic mass at z<0.15. We then combine empirical scaling relations for the observed ``multiphase ratio'', N_HI_/NOVI_∝N0.9±0.1^_HI_, and for hydrogen overdensity in cosmological simulations, N_HI_∝δ0.7^_H, with the H I photoionization correction to derive the mean oxygen metallicity, Z_O~(0.09Z_☉)(f_OVI_/0.2)^–1 in the low-z multiphase gas. Given the spread in the empirical relations and in f_OVI_, the baryon content in the O VI WHIM could be as large as 10%. Our survey is based on a large improvement in the number of O VI absorbers (40 vs. 10) and total redshift path length (Δz~2.2 vs. Δz~0.5) compared to earlier surveys.