A comprehensive description of the spin dynamics underlying the formation of Ortho-Deuterium Induced Polarization (ODIP) is presented. ODIP can serve as a tool for enhancing Nuclear Magnetic Resonance (NMR) signals of 2H nuclei, being important probes of molecular structure and dynamics. To produce ODIP, in the first step, the D2 gas is brought to thermal equilibrium at low temperature, here 30 K, so that the ortho-component, corresponding to the total spin of the 2H nuclei equal to 0 and 2, is enriched, here to 92%. In the second step, the orthodeuterium molecule is attached to a substrate molecule using a suitable hydrogenation catalyst such that the symmetry of the two 2H nuclei is broken. As a result, the non-thermal spin order of orthodeuterium is converted into enhancement of observable NMR signals. In this work, we perform a theoretical study of ODIP and calculate the shape of ODIP spectra and their dependence on the magnetization flip angle. These results are compared with experiments performed for a number of substrates; good agreement between experimental and calculated ODIP spectra is found. We also discuss the performance of NMR techniques for converting anti-phase ODIP spectral patterns into in-phase patterns, which are more suitable for signal detection and for transferring ODIP to heteronuclei, here to 13C spins. Experimental procedures reported here allowed us to reach signal enhancement factors of more than 1000 for 2H nuclei in the liquid phase. These results are useful for extending the scope of spin hyperpolarization to the widely used 2H nuclei.