  In this paper we use ultra-violet (UV) and optical HST photometry in five
bands, and an extensive set of spectral evolutionary synthesis scenarios to
investigate the age and masses of 124 star clusters in the luminous blue
compact galaxy ESO338-IG04 (Tololo 1924-416). The very small internal reddening
makes ESO 338-IG04 an excellent laboratory for studying the formation of
massive star clusters. We have used the star clusters to trace the temporal and
spatial evolution of the starburst, and to put constraints on the star
formation activity over a cosmological time-scale. The present starburst has
been active for about 40 Myr. A standard Salpeter initial mass function (IMF)
extending up to 120 solar masses provides the best fit to the data, although a
flatter IMF cannot be excluded. The compact star clusters provide 30-40 percent
of the UV luminosity and star formation activity. We find no evidence for dust
obscuration even among the youngest (< 1 Myr) clusters. The fraction of stellar
mass contained in compact star clusters is found to be several percent, which
is an unusually high value. The intermediate age clusters show a flattened
space distribution which agrees with the isophotal shape of the galaxy, whereas
the oldest clusters seem to have a spherical distribution.(abridged)
