Optical turbulence occurring in the oceanic waters may be detrimental for light beams used in the short-link communication and sensing systems, and, in particular, in underwater LIDARs. We develop a theory capable of predicting the passage of light beams through the bi-static LIDAR systems, for a wide variety of optical waves, including partially coherent and partially polarized, and for a wide family of targets. Our theoretical framework is based on the Huygens-Fresnel integral adopted to random media and optical systems described by the $4\times4$ ABCD matrices. The treatment of oceanic turbulence relies on the recently introduced power spectrum model of the fluctuating refractive-index [Opt. Express 27, 27807 (2019)] capable of accounting for different average temperatures of water. We first analyze the evolution of the second-order beam statistics such as the spectral density and the degree of coherence of the beam on its single pass propagation and then incorporate this knowledge into the analysis of the bi-static LIDAR returns.