We explore the production and escape of ionizing photons in young galaxies by investigating the ultraviolet and optical emission-line properties of models of ionization-bounded and density-bounded H regions, active-galactic-nucleus (AGN) narrow-line regions and radiative shocks computed all using the same physically-consistent description of element abundances and depletion on to dust grains down to very low metallicities. We compare these models with a reference sample of metal-poor star-forming galaxies and Lyman-continuum (LyC) leakers at various redshifts, which allows the simultaneous exploration of more spectral diagnostics than typically available at once for individual subsamples. We confirm that current single-and binary-star population synthesis models do not produce hard-enough radiation to account for the high-ionization emission of the most metal-poor galaxies. Introducing either an AGN or radiative-shock component brings models into agreement with observations. A published model including X-ray binaries is an attractive alternative to reproduce the observed rise in He λ4686/Hβ ratio with decreasing oxygen abundance in metal-poor star-forming galaxies, but not the high observed He λ4686/Hβ ratios of galaxies with large EW(Hβ). A source of harder ionizing radiation appears to be required in these extreme objects, such as an AGN or radiative-shock component, perhaps linked to an initial-mass-function bias toward massive stars at low metallicity. This would also account for the surprisingly high [O ]/[O ] ratios of confirmed LyC leakers relative to ionization-bounded models. We find no simple by-eye diagnostic of the nature of ionizing sources and the escape of LyC photon, which require proper simultaneous fits of several lines to be discriminated against.