PKS 0537-441, a bright gamma -ray emitting blazar, was observed at radio, optical, UV and X-ray frequencies during various EGRET pointings, often quasi-simultaneously. In 1995 the object was found in an intense emission state at all wavelengths. BeppoSAX observations made in 1998, non-simultaneously with exposures at other frequencies, allow us to characterize precisely the spectral shape of the high energy blazar component, which we attribute to inverse Compton scattering. The optical-to-gamma -ray spectral energy distributions at the different epochs show that the gamma -ray luminosity dominates the bolometric output. This, together with the presence of optical and UV line emission, suggests that, besides the synchrotron self-Compton mechanism, the Compton upscattering of photons external to the jet (e.g., in the broad line region) may have a significant role in the production of high energy radiation. The multiwavelength variability can be reproduced by changes of the plasma bulk Lorentz factor. The spectrum secured by IUE in 1995 appears to be partially absorbed shortward of ~ 1700 Å. However, this signature is not detected in the HST spectrum taken during a lower state of the source. The presence of intervening absorbers is not supported by optical imaging and spectroscopy of the field.