The strong coupling between excitons and single plasmonic nanocavities enables plexcitonic states in nanoscale systems at room temperature. Here we demonstrate the strong coupling of surface plasmon modes of metal nanowires and excitons in monolayer semiconductors, with Rabi splitting manifested in both scattering and photoluminescence (PL) spectra. By utilizing the propagation properties of surface plasmons on the nanowires, the PL emitted through the scattering of plasmon-exciton hybrid modes is extracted. The analytically calculated scattering and PL spectra well reproduce the experimental results. These findings unify the scattering and PL spectra in the plexcitonic system and eliminate the ambiguities of PL emission, shedding new light on understanding the rich spectral phenomena in the plasmon-exciton strong coupling regime.