We report magnetic, dielectric, and magnetodielectric responses of the pure monoclinic bulk phase of partially disordered La2NiMnO6, exhibiting a spectrum of unusual properties and establish that this compound is an intrinsically multiglass system with a large magnetodielectric coupling (8%-20%) over a wide range of temperatures (150-300 K). Specifically, our results establish a unique way to obtain colossal magnetodielectricity, independent of any striction effects, by engineering the asymmetric hopping contribution to the dielectric constant via the tuning of the relative-spin orientations between neighboring magnetic ions in a transition-metal oxide system. We discuss the role of antisite (Ni-Mn) disorder in emergence of these unusual properties.