Ba ₂ YIrO ₆ , a Mott insulator, with four valence electrons in Ir ⁵⁺ d-shell (5d ⁴ ) is supposed to be non-magnetic, with J _eff = 0, within the atomic physics picture. However, recent suggestions of non-zero magnetism have raised some fundamental questions about its origin. We focus on the phonon dynamics, probed via Raman scattering, as a function of temperature and different incident photon energies, as an external perturbation. Our studies reveal strong renormalization of the phonon self-energy parameters and integrated intensity for first-order modes, especially redshift of the few first-order modes with decreasing temperature and anomalous softening of modes associated with IrO ₆ octahedra, as well as high energy Raman bands attributed to the strong anharmonic phonons and coupling with orbital excitations. The distinct renormalization of second-order Raman bands with respect to their first-order counterpart suggest that higher energy Raman bands have significant contribution from orbital excitations. Our observation indicates that strong anharmonic phonons coupled with electronic/orbital degrees of freedom provides a knob for tuning the conventional electronic levels for 5d-orbitals, and this may give rise to non-zero magnetism as postulated in recent theoretical calculations with rich magnetic phases.