  We investigate the electronic and magnetic properties as well as lattice
dynamics and spin-phonon coupling of $\beta$-Na$_{0.33}$V$_2$O$_5$ using
temperature-dependent Raman scattering, dc-magnetization and dc-resistivity,
x-ray photoemission, and absorption spectroscopy. The Rietveld refinement of
XRD pattern with space group C2/m confirms the monoclinic structure. The
analysis of temperature-dependent Raman spectra in a temperature range of
13--673~K reveals an anharmonic dependence of the phonon frequency and full
width at half maximum, which is accredited to the symmetric phonon decay.
However, below about 40 K, the hardening of the phonon frequency beyond
anharmonicity is attributed to the spin-phonon coupling. Interestingly, the
estimated effective magnetic moment $\mu_{\rm eff}=$ 0.63~$\mu_B$ from the
magnetization data manifests a mixed-valence state of V ions in 4+ (18$\pm$1\%)
and 5+ (82$\pm$1\%). A similar ratio of V$^{4+}$ to V$^{5+}$ is also observed
in the x-ray photoemission and x-ray absorption near-edge spectra and that is
found to be consistent with the sample stoichiometry. In addition, the V$^{4+}$
ions are distributed between different vanadium (V1 and V3) sites. The analysis
of extended x-ray absorption fine structure at different V-sites gives the
corresponding V--O bond lengths, which are utilized in the assignment of Raman
modes. Moreover, the temperature-dependent resistivity resembles a
semiconducting behavior where the charge carrier transport is facilitated by
the band conduction at higher temperatures and via hopping $\le$260~K.
