While there is now a consensus that X-ray binaries (XRBs) are the dominant X-ray sources in the early Universe and play a significant role during the epoch of heating of the intergalactic medium (IGM), recent studies report contradicting results regarding their contribution in the nebular emission of local Universe galaxies. Ultraluminous X-ray sources (ULXs), which dominate the X-ray budget of normal galaxies, may be important interstellar-medium (ISM) ionizing sources. However, their output in the extreme-ultraviolet (EUV) and soft X-ray part of the spectrum remains observationally unconstrained. In this paper, we predict the ionizing and heating power from ULX populations under the geometrical beaming scenario, and three models describing the emission from super-critical accretion disks. We find that our theoretical spectra for ULX populations cannot (can) explain the He II (Ne V) emission observed in some galaxies, with their contribution being less (more) important than the underlying stellar population. Stochastic fluctuations in the number of ULXs may allow for equal contributions in the He II emission, in a fraction of galaxies. We provide average spectra of ULX populations as an input to local, and early-Universe studies. We find that the soft X-ray emission arising from super-critical accretion is significant for the heating of the IGM, and consistent with recent constraints from the 21-cm cosmic signal. Based on the dependence on the adopted compact-object (CO) mass and accretion model, we encourage efforts in modeling ULX spectra via simulations, and their combination with detailed binary population synthesis models.Key words: accretion / accretion disks / X-rays: binaries / X-rays: ISM / X-rays: galaxies / ultraviolet: galaxies⋆ Full Table 1 is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/665/A28