We present a study of the local atomic environment of the oxygen atoms in the aqueous solutions of NaOH and HCl under simultaneous high-temperature and high-pressure conditions. Experimental nonresonant X-ray Raman scattering core-level spectra at the oxygen K-edge show systematic changes as a function of temperature and pressure. These systematic changes are distinct for the two different solutes and are described well by calculations within the Bethe-Salpeter formalism for snapshots from ab initio molecular dynamics simulations. The agreement between experimental and simulation results allows us to use the computations for a detailed fingerprinting analysis in an effort to elucidate the local atomic structure and hydrogen-bonding topology in these relevant solutions. We observe that both electrolytes, especially NaOH, enhance hydrogen bonding and tetrahedrality in the water structure at supercritical conditions, in particular in the vicinity of the hydration shells. This effect is accompanied with the association of the HCl and NaOH molecules at elevated temperatures.