jats:titleABSTRACT</jats:title> jats:pThe early Universe, spanning 400 000 to 400 million years after the big bang (z ≈ 1100–11), has been left largely unexplored as the light from luminous objects is too faint to be observed directly. While new experiments are pushing the redshift limit of direct observations, measurements in the low-frequency radio band promise to probe early star and black hole formation via observations of the hydrogen 21-cm line. In this work, we explore synergies between 21-cm data from the HERA and SARAS 3 experiments and observations of the unresolved radio and X-ray backgrounds using multiwavelength Bayesian analysis. We use the combined data set to constrain properties of Population II and Population III stars as well as early X-ray and radio sources. The joint fit reveals a 68 percentile disfavouring of Population III star formation efficiencies $\gtrsim 5.7 per cent$. We also show how the 21-cm and the X-ray background data synergistically constrain opposite ends of the X-ray efficiency prior distribution to produce a peak in the 1D posterior of the X-ray luminosity per star formation rate. We find (at 68 per cent confidence) that early galaxies were likely 0.3–318 times as X-ray efficient as present-day starburst galaxies. We also show that the functional posteriors from our joint fit rule out global 21-cm signals deeper than ≲−203 mK and power spectrum amplitudes at k = 0.34 h Mpc−1 greater than $\Delta 212\gtrsim 946 \mathrm{mK}2$ with 3σ confidence.</jats:p>