  The presence of very massive stars (VMS, masses $>100$ M$_{\odot}$) is now
firmly established in the local group, nearby galaxies, and out to cosmological
distances. If present, these stars could boost the UV luminosity and ionizing
photon production of galaxies, helping thus to alleviate the overabundance of
UV-bright galaxies found with the JWST at high-redshift. Combing consistent
stellar evolution and atmosphere models tailored to VMS we compute spectral
energy distributions (SEDs) for a large set of models. We find that VMS
contribute significantly to the UV luminosity and Lyman continuum of young
stellar populations, and they are characterized by strong stellar HeII1640
emission, with EW(HeII) up to 4-8 Ang at young ages or $\sim 2.5-4$ Ang for
constant SFR. For IMFs with a Salpeter slope, the boost of the UV luminosity is
relatively modest. However, small changes in the IMF slope (e.g.~from
$\alpha_2=-2.35$ to $-2$) lead to large increases in $L_{UV}$ and the ionizing
photon production $Q$. Emission line strengths and the ionizing photon
efficiency $\xi_{\rm ion}$ are also increased with VMS. Interestingly, SEDs
including VMS show smaller Lyman breaks, and the shape of the ionizing spectra
remain unaltered up to $\sim 35$ eV, but becomes softer at higher energies. We
derive and discuss the maximum values quantities such as $L_{UV}$ per stellar
mass or unit SFR, and $\xi_{\rm ion}$, $Q$ can reach when VMS are included, and
we show that these values become essentially independent of the IMF. We propose
observational methods to test for VMS and constrain the IMF. Finally, using
JWST observations, we examine if high-redshift galaxies show some evidence of
the presence of VMS and signs of non-standard IMFs. Very top-heavy IMFs can be
excluded on average, but the IMF could well extend into the regime of VMS and
be flatter than Salpeter in the bulk of high-$z$ galaxies. (abridged)
