In this work, we investigate the correlation between morphology, composition, and the mechanical properties of metallic amorphous tungsten-oxygen and amorphous tungsten-oxide films deposited by Pulsed Laser Deposition. This correlation is investigated by the combined use of Brillouin Spectroscopy and the substrate curvature method. The stiffness of the films is strongly affected by both the oxygen content and the mass density. The elastic moduli show a decreasing trend as the mass density decreases and the oxygen-tungsten ratio increases. A plateaux region is detected in correspondence of the transition between metallic and oxide films. The compressive residual stresses, moderate stiffness and high local ductility that characterize compact amorphous tungsten-oxide films make them promising for applications involving thermal or mechanical loads. The coefficient of thermal expansion is quite high (i.e. 8.9 $cdot$ 10$^{-6}$ K$^{-1}$), being strictly correlated to the amorphous structure and stoichiometry of the films. Under thermal treatments they show a quite low relaxation temperature (i.e. 450 K). They crystallize into the $gamma$ monoclinic phase of WO$_3$ starting from 670 K, inducing an increase by about 70% of material stiffness.