The unconventional electronic ground state of Sr_{3}IrRuO_{7} is explored via resonant x-ray scattering techniques and angle-resolved photoemission measurements. As the Ru content approaches x=0.5 in Sr_{3}(Ir_{1-x}Ru_{x})_{2}O_{7}, intermediate to the J_{eff}=1/2 Mott state in Sr_{3}Ir_{2}O_{7} and the quantum critical metal in Sr_{3}Ru_{2}O_{7}, a thermodynamically distinct metallic state emerges. The electronic structure of this intermediate phase lacks coherent quasiparticles, and charge transport exhibits a linear temperature dependence over a wide range of temperatures. Spin dynamics associated with the long-range antiferromagnetism of this phase show nearly local, overdamped magnetic excitations and an anomalously large energy scale of 200 meV-an energy far in excess of exchange energies present within either the Sr_{3}Ir_{2}O_{7} or Sr_{3}Ru_{2}O_{7} solid-solution end points. Overdamped quasiparticle dynamics driven by strong spin-charge coupling are proposed to explain the incoherent spectral features of the strange metal state in Sr_{3}IrRuO_{7}.