Modern design of superior multi-functional alloys composed of several principal components requires in-depth studies of their local structure for developing desired macroscopic properties. Herein, peculiarities of atomic arrangements on the local scale and electronic states of constituent elements in the single-phase face-centered cubic (fcc)- and body-centered cubic (bcc)-structured high-entropy Al_x-CrFeCoNi alloys (x = 0.3 and 3, respectively) are explored by element-specific X-ray absorption spectroscopy in hard and soft X-ray energy ranges. Simulations based on the reverse Monte Carlo approach allow to perform a simultaneous fit of extended X-ray absorption fine structure spectra recorded at K absorption edges of each 3d constituent and to reconstruct the local environment within the first coordination shells of absorbers with high precision. The revealed unimodal and bimodal distributions of all five elements are in agreement with structure-dependent magnetic properties of studied alloys probed by magnetometry. A degree of surface atoms oxidation uncovered by soft X-rays suggests different kinetics of oxide formation for each type of constituents and has to be taken into account. X-ray magnetic circular dichroism technique employed at L_2,3 absorption edges of transition metals demonstrates reduced magnetic moments of 3d metal constituents in the sub-surface region of in situ cleaned fcc-structured Al_0.3-CrFeCoNi compared to their bulk values. Extended to nanostructured versions of multicomponent alloys, such studies would bring new insights related to effects of high entropy mixing on low dimensions.