  Extending the electromagnetic and gravitational radiations from binary black
holes with electric and magnetic charges in circular orbits in Phys. Rev. D
{\bf 102}, 103520 (2020), we calculate the total emission rates of energy and
angular momentum due to gravitational and electromagnetic radiations from
dyonic binary black holes in precessing elliptical orbits. It is shown that the
emission rates of energy and angular momentum due to gravitational and
electromagnetic radiations have the same dependence on the conic angle for
different orbits. Moreover, we obtain the evolutions of orbits and find that a
circular orbit remains circular while an elliptic orbit becomes quasi-circular
due to electromagnetic and gravitational radiations. Using the evolution of
orbits, we derive the waveform models for dyonic binary black hole inspirals
and show the amplitudes of the gravitational waves for dyonic binary black hole
inspirals differ from those for Schwarzschild binary black hole inspirals,
which can be used to test electric and magnetic charges of black holes.
