We analyze the physical conditions, chemical composition, and other properties of the photoionized Herbig-Haro (HH) object HH 204 through Very Large Telescope echelle spectroscopy and Hubble Space Telescope imaging. We kinematically isolate the high-velocity emission of HH 204 from the emission of the background nebula and study the subarcsecond distribution of physical conditions and ionic abundances across the HH object. We find that low- and intermediate-ionization emission arises exclusively from gas at photoionization equilibrium temperatures, whereas the weak high-ionization emission from HH 204 shows a significant contribution from higher-temperature shock-excited gas. We separately derive the ionic abundances of HH 204, the emission of the Orion Nebula, and the fainter diffuse blue layer. In HH 204, the O+ abundance determined from collisional excited lines matches the one based on recombination lines, while the O2+ abundance is very low, so that the oxygen abundance discrepancy is zero. The ionic abundances of Ni and Fe in HH 204 have similar ionization and depletion patterns, with total abundances that are a factor of 3.5 higher than in the rest of the Orion Nebula due to dust destruction in the bow shock. We show that a failure to resolve the kinematic components in our spectra would lead to significant error in the determination of chemical abundances (for instance, a 40% underestimate of O), mainly due to incorrect estimation of the electron density.