In this paper we report CCD photometry in broad band B, R, and I colors, as well as in the Hα, for a sample of eight HII galaxies with strong radio emission. In addition, we present new radio continuum observations in the frequency range between 8 and 15GHz. For seven of these galaxies, previous radio continuum observations have been reported by Deeg et al. (1993ApJ...410..626D); data on Haro 1 are presented here for the first time. Their unusual radio spectra, according to Deeg et al., are a consequence of rapidly changing star formation rates in their past. An independent verification of this conclusion is the motivation for the optical observations reported here. Their interpretation is the subject of the next article in this series. The new radio measurements confirm the interpretation of the radio spectra by Deeg et al. In combination with extinction corrected Hα fluxes, the new radio measurements allow the determination of thermal radio fluxes - a fundamental parameter for star formation rates - with higher reliability than is possible from one wavelength domain alone. Overlays of optical observations at different colors with radio maps, as well as a search of the literature, indicates that all sample galaxies are in interacting environments, which is a possible prerequisite for the strength of the radio emission and star formation observed in these galaxies.