The HyGAL Stratospheric Observatory for Infrared Astronomy (SOFIA) legacy program aims at characterizing the interstellar medium in the Milky Way using hydrides, [CII], and [OI] absorption lines with the 2.7m SOFIA telescope toward twenty-five submillimeter-bright Galactic star-forming regions. As part of HyGAL, we investigated correlations among the known H_2_ tracers- CH and OH from SOFIA observations, and HCO^+^ and CCH from ancillary absorption line data from ground-based telescopes. We also examined the abundance variation of neutral atomic oxygen, [OI], observed in absorption. CH, OH, HCO^+^, and CCH all exhibit strong mutual correlations. OH in particular shows tight correlations with HCO^+^ and CCH, reflecting their linked chemical and physical pathways. Column density ratios among these H_2_ tracers are consistent with previous measurements in local diffuse clouds and remain uniform across Galactic environments and velocity intervals. The gas phase oxygen abundance relative to total hydrogen, <X(O)>=N(O)/N(Htotal), is (3.09+/-0.64)x10^-4^, slightly below the elemental solar value but consistent with the previous observations measuring gas-phase abundances. We also find that N(HI) decreases toward the regions where the molecular fraction exceeds f^N^_H2_~0.5, marking the onset of the molecular phase. While the atomic oxygen abundance remains roughly constant, the abundances of OH, HCO^+^, and CCH increase with the molecular fraction. Gas traced by the HCO^+^ absorption corresponds to higher molecular fractions than that traced by HI and hydride ions, highlighting density variations in the diffuse-to-translucent ISM along different lines of sight.