Aims: We have performed a comprehensive multiwavelength analysis of a sample of 20 starburst galaxies that show the presence of a substantial population of massive stars. The main aims are the study of the massive star formation and stellar populations in these galaxies, and the role that interactions with or between dwarf galaxies and/or low surface companion objects have in triggering the bursts. In this series of papers, we present our new optical and near-infrared photometric and spectroscopic observations, and complete with data at other wavelengths (X-ray, far-infrared, and radio) available in the literature. In this paper, the first in the series, we analyze the morphology, stellar population age, and star-formation rate of each system. Methods: We completed new deep optical and NIR broad-band images, as well as the new continuum-subtracted Hα maps, of our sample of Wolf-Rayet galaxies. We analyze the morphology of each system and its surroundings and quantify the photometric properties of all important objects. All data were corrected for both extinction and nebular emission using our spectroscopic data. The age of the most recent star-formation burst is estimated and compared with the age of the underlying older low-luminosity population. The Hα-based star-formation rate, number of O7V equivalent stars, mass of ionized gas, and mass of the ionizing star cluster are also derived. Results: We found interaction features in many (15 up to 20) of the analyzed objects, which were extremely evident in the majority. We checked that the correction for nebular emission to the broad-band filter fluxes is important in compact objects and/or with intense nebular emission to obtain realistic colors and compare with the predictions of evolutionary synthesis models. The estimate of the age of the most recent star-formation burst is derived consistently. In general, the Hα-based star formation rate agrees with the estimates given by independent multiwavelength methods. With respect to the results found in individual objects, we remark the strong Hα emission found in IRAS 08208+2816, UM 420, and SBS 0948+532, the detection of a double-nucleus in SBS 0926+606A, a possible galactic wind in Tol 9, and one (two?) nearby dwarf star-forming galaxies surrounding Tol 1457-437. Based on observations made with NOT (Nordic Optical Telescope) and INT (Isaac Newton Telescope) operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway and Sweden (NOT) or the Isaac Newton Group (INT) in the Spanish Observatorio del Roque de Los Muchachos of the Instituto de Astrofísica de Canarias. Based on observations made at the Centro Astronómico Hispano Alemán (CAHA) at Calar Alto, operated by the Max-Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC). Tables 2-7, Figs. 1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 33, 35 and Appendices are only available in electronic form at http://www.aanda.org