The electronic structure of the quasi-one-dimensional vanadium beta-bronze \ensuremath{\beta}-Sr${}_{0.17}$V${}_{2}$O${}_{5}$ has been measured in detail using soft x-ray absorption spectroscopy, x-ray emission spectroscopy, and resonant inelastic soft x-ray scattering. Together, these measurements have been used to derive the experimental site-resolved ($k$-integrated) band structure of a material whose electronic structure is difficult to obtain from first principles. The occupied states, probed by x-ray emission measurements, demonstrate the O 2$p$--V 3$d$ bonding hybridization at the bottom of the O 2$p$ band, with the V 3${d}_{xy}$ ``magnetic orbitals'' well separated in energy. These results are consistent with the carriers being small polarons. The strong anisotropy in the absorption spectrum is used to identify the energy and character of the unoccupied states. Additionally, absorption measurements at the V $L$-edge are compared with atomic multiplet calculations, clarifying the interpretation of the experimental multiplet structure and consistent with the presence of both V${}^{5+}$ and V${}^{4+}$ species. Site-specific electronic excitations, probed by resonant inelastic x-ray scattering at the V $L$-edge, are observed at an energy of 1.1 eV, and are suggested to correspond to transitions from the partially filled ${d}_{xy}$ magnetic orbital into the unoccupied ${d}_{xy,yz}$ orbitals.