A sample of actively star forming H II galaxies has been observed in the radio continuum and several optical bands. These galaxies are currently undergoing very active star formation and have been selected on the basis of strong radio continuum emission. Most of the galaxies are irregular and have been associated with merger or interaction events, which may have triggered the star formation and the radio emission. Radio continuum observations at 0.32 GHz, 1.5 GHz, and in the range of 8-15 GHz were obtained at the NRAO-VLA, to determine their radio spectra. Several of the spectra were found to flatten towards lower frequencies, which is unusual. Surface and aperture photometry was obtained in the B,R, and I bands and in the H-alpha emission line. Radio emission, absorption, and relativistic electron loss mechanisms are reviewed and their suitability to account for the observed spectral shapes is discussed. Energy equipartition calculations led to galaxy magnetic fields of 10-30 mu-G; the radiation density inside the H II regions has been derived by a new method and was found to be in the range of 2 to 15 eVJcm-3. Mechanisms which may account for the observed radio spectra were fitted to the radio continuum data. The spectra resulting from a time variable relativistic electron injection ('synchrotron aging') have been calculated over a greater range of parameters than previously published. Fits of these spectra show variations of the injection rate with time scales of the order of a few Myrs. A fit based on free-free absorption uses the emission measure to balance both free-free absorption and thermal emission, thereby constraining the maximum size of the thermally emitting region. This permits a direct comparison with the optical H-alpha observations which typically show H II regions with sizes between 0.5 and 1 kpc. The fits allowed the derivation of a variety of physical parameters, such as the electron density, which is typically between 10 and 60 cm-3, and the emission measure, which is of the order of a few 105 pc cm-6. Fits of different mechanisms may describe the same spectrum well, thus, in some cases, a unique determination of a particular mechanism is not possible, although an estimate for its likelihood can be made. Parts of this work have been published by Deeg et al. (1993, ApJ 410, 626). The fraction of thermal emission in the galaxies has been determined with a higher reliability than usual by combining radio, H-alpha, and UV data. A correlation between the fraction of thermal emission and the size, as well as the total luminosity of the galaxies has been found. A simple model of relativistic electron diffusion losses-dependent on a galaxies' size-can reproduce the observed correlation well; its suitability and limits are discussed. This correlation may lead to a better understanding between the supernova rate in a galaxy and the expected non-thermal emission, a relation which is currently only very poorly known. Star formation rates based on thermal and nonthermal radio and FIR emission all indicate star formation which is enhanced during the last 10^6-7 years as compared to the long term (1 Gyr) rates based on B band photometry. `Synchrotron aging', optical colors and the thermal to FIR ratio were used to derive typical ages of star formation. Based on the star formation rates and the age indicators, the galaxies were sorted into an sequence of their starbursts ages. The physical picture of a region in which star formation, subsequent SN explosions, and the resulting nonthermal radio emission takes place, can be accounted for well, by comparing the different star formation estimators which are based on a variety of radiative processes and across three regions of the electromagnetic spectrum.