We examine the structural, vibrational, and transport properties of EuAg4As2 single crystals under pressures up to 28.8-41.8 GPa, aiming to trace the evolution of the structural distortion near Ts~130 K and the two magnetic transitions at TN1~15 K and TN2~9 K. Under ambient conditions, a Raman-active phonon mode centered at 157 cm-1 is observed and identified as having A1g symmetry, and its temperature evolution shows no discernible anomaly across these three transitions. Under pressure, combined synchrotron x-ray diffraction and Raman measurements reveal two structural distortions at Pc1~7 GPa and Pc2~17 GPa. Structural refinements and bond-valence-sum analysis suggest that these transitions mainly involve successive discontinuous modifications of the Ag-As tetrahedra, without changing the average crystal symmetry. Distinct transport and magnetic responses accompany these structural distortions: for P<Pc1, Ts increases while its resistivity anomaly is suppressed, and TN1 and TN2 gradually increases; for Pc1<P<Pc2, high-temperature ferromagnetic-like and low-temperature antiferromagnetic-like states emerge; and for P>Pc2, the resistivity becomes metallic-like, with only a faint broad kink and very weak magnetoresistance comparable to that of traditional metals.