We used magnetohydrodynamical cosmological simulations to investigate the cross-correlation between different observables (i.e. X-ray emission, Sunyaev-Zeldovich (SZ) signal at 21 cm, HI temperature decrement, diffuse synchrotron emission, and Faraday Rotation) as a probe of the diffuse matter distribution in the cosmic web. We adopt a uniform and simplistic approach to produce synthetic observations at various wavelengths, and we compare the detection chances of different combinations of observables correlated with each other and with the underlying galaxy distribution in the volume. With presently available surveys of galaxies and existing instruments, the best chances to detect the diffuse gas in the cosmic web outside of haloes is by cross-correlating the distribution of galaxies with SZ observations. We also find that the cross-correlation between the galaxy network and the radio emission or the Faraday Rotation can already be used to limit the amplitude of extragalactic magnetic fields, well outside of the cluster volume usually explored by existing radio observations, and to probe the origin of cosmic magnetism with the future generation of radio surveys.