Tungsten oxide (WOx) films grown on tungsten (W) are characterized by depth-resolved Doppler-broadening spectroscopy (DBS) and positron-annihilation lifetime spectroscopy (PALS) as primary analytical methods. The WOx films are prepared on W(111) monocrystals using either exposure to air, electrochemical, or thermal oxidation procedures, chosen according to the desired thickness. We calculate the lifetime of positrons in the bulk of WOx and in different types of vacancies using the atomic superposition (AtSup) method. These give the size required for a multivacancy in WOx needed for it to be identifiable by PALS. In our experiments, we identified a distinct positron lifetime of 325ps in the thin oxide layer on W exposed to air. This value overlaps with that of multivacancy sites in W and, hence, should be taken into account in future PALS studies of radiation-induced defects in W.