The state of supranuclear matter in compact stars remains puzzling, and it is argued that pulsars could be strangeon stars. What would happen if binary strangeon stars merge? This kind of merger could result in the formation of a hyper-massive strangeon star, accompanied by bursts of gravitational waves and electromagnetic radiation (and even a strangeon kilonova explained in the paper). The tidal polarizability of binary strangeon stars is different from that of binary neutron stars, because a strangeon star is self-bound on the surface by the fundamental strong force while a neutron star by the gravity, and their equations of state are different. Our calculation shows that the tidal polarizability of merging binary strangeon stars is favored by GW170817. Three kinds of kilonovae (i.e., of neutron, quark and strangeon) are discussed, and the light curve of the kilonova AT 2017gfo following GW170817 could be explained by considering the decaying strangeon nuggets and remnant star spin-down. Additionally, the energy ejected to the fireball around the nascent remnant strangeon star, being manifested as a gamma-ray burst, is calculated. It is found that, after a prompt burst, an X-ray plateau could follow in a timescale of 10(2) - 10(3) s. Certainly, the results could be tested also by further observational synergies between gravitational wave detectors (e.g., Advanced LIGO) and X-ray telescopes (e.g., the Chinese HXMT satellite and eXTP mission), and especially if the detected gravitational wave form is checked by peculiar equations of state provided by the numerical relativistical simulation.