We present the results of a large survey of H i, O vi, and C iii absorption lines in the low-redshift (z < 0:3) intergalactic medium (IGM). We begin with 171 strong Ly absorption lines (W k ! 80 m8) in 31 AGN sight lines studied with the Hubble Space Telescope and measure corresponding absorption from higher order Lyman lines with FUSE. Higher order Lyman lines are used to determine N H i and b H i accurately through a curve-of-growth (COG) analysis. We find that the number of H i absorbers per column density bin is a power-law distribution,, with H i ¼ 1:68 AE 0:11. We made 40 detections of O vi kk1032, 1038 and 30 detections of C iii k977 out of 129 and 148 potential absorbers, respectively. The column density distribution of C iii absorbers has C iii ¼ 1:68 AE 0:04, similar to H i but not as steep as O vi ¼ 2:2 AE 0:1. From the absorption-line frequency, dN C iii /dz ¼ 12 þ3 À2 for W k (C iii) > 30 m8, we calculate a typical IGM absorber size r 0 $ 400 kpc, similar to scales derived by other means. The COGderived b-values show that H i samples material with T < 10 5 K, incompatible with a hot IGM phase. By calculating a grid of CLOUDY models of IGM absorbers with a range of collisional and photoionization parameters, we find it difficult to simultaneously account for the O vi and C iii observations with a single phase. Instead, the observations require a multiphase IGM in which H i and C iii arise in photoionized regions, while O vi is produced primarily through shocks. From the multiphase ratio N H i /N C iii , we infer the IGM metallicity to be Z C ¼ 0:12 Z , similar to our previous estimate of Z O ¼ 0:09 Z from O vi.