We report the results of neutron diffraction, ac and dc magnetization, heat-capacity, complex permittivity, and pyrocurrent measurements on an oxide, Li3NiRuO5, hitherto not paid much attention in the literature, except for a previous report on its promising electrochemical performance. We emphasize on the following findings: (i) Observation of re-entrant spin-glass behavior; that is, this oxide undergoes ferrilmagnetic ordering below 8- K, entering spin-glass regime around 12 K. (ii) There is no prominent feature in the complex dielectric permittivity (in particular, at the magnetic transitions) in the absence of external magnetic field, indicative of the absence of ferroelectricity. However, there is a distinct evidence for magneto-dielectric (MDE) coupling. The sign of MDE coupling also changes as the sample is cooled from ferrimagnetic state to spin-glass regime. (iii) There are pyroelectric anomalies in the vicinity of 30-70 K, presumably from thermally stimulated depolarization current.