ABSTRACT We present the study of multimessenger signatures of massive black hole (MBH) binaries residing in the centres of galaxy merger remnants. In particular, we first focus on the gravitational wave background (GWB) produced by an ensemble of MBH binary inspirals in the frequency range probed by the Pulsar Timing Array (PTA) experiments. The improved estimates of the characteristic strain were obtained with the inclusion of environmental effects on the MBH binary orbital decay within the galaxy merger remnants, added in post-processing to the semi-analytical model of galaxy formation and evolution SHARK. Secondly, we explore two, intriguing in terms of the MBH binary evolution studies, hypotheses aiming to explain the origins of X-shaped radio galaxies – a peculiar type of objects with double lobe structures, constituting approximately 6–10 per cent of known radio loud galaxies. The two considered scenarios involve either an abrupt change in the jet direction after an MBH merger (a spin-flip) or an unresolved close binary, where each of the two components produces a jet. We find that the estimated GWB amplitude at the reference frequency $f_0=1 \, {\rm yr}^{-1}$ is in the range of $A_{\rm { yr^{-1}}} = 1.20\times 10^{-15}{\!-\!}1.46\times 10^{-15}$, which is 50 per cent lower than the strain of the signal detected by the PTA experiments. We also show that the spin-flip scenario considered in gas-poor mergers reproduces the observed properties of X-shaped radio galaxies well in terms of flip angle, redshift, and luminosity distributions.