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Structural and lattice dynamical behavior of novel spin-orbit entangled 5d-Mott insulator Sr₂IrO₄ and Sr₂Ir_1-xCo_xO₄ have been investigated by pressure and temperature dependent Raman scattering. Anomalies in phonon intensities, energies, and line-widths of Sr₂IrO₄ were observed at 17, 30 and 40 GPa, with no detected structural phase transition up to 45 GPa. Our findings reveal a transition of Ir⁴⁺: 5d⁵ electrons from the J_eff = 1/2 configuration below 17 GPa to a competing disentangled state with a hole in a xz ± iyz orbital above 40 GPa, crossing a mixed disordered phase at intermediate pressure. A Fano-interference is also detected in pressure range between 17 to 40 GPa, revealing that the low-energy orbital dynamics of Ir⁴⁺ (5d⁵) electrons is impacted by the transitions. Temperature dependent (20 - 300K) Raman scattering of Sr₂IrO₄ and Sr₂Ir_1-xCo_xO₄ shows an anomalous softening (~7%) of A_1g mode at 276 cm^-1. This anomalous change could be due to the additional contribution of spin-phonon coupling along with anharmonicity. Fano-interference is detected in Sr₂Ir_1-xCo_xO₄ throughout the studied temperature range, however this phenomena is absent in Sr₂IrO₄, indicating the formation of an electronic continuum in Sr₂IrO₄ due to Co substitution.