  We investigate the correction to the potential that gives rise to the bound
orbits and radiation from non-spinning inspiralling binary black holes in a
dark matter environment consisting of axion-like particles and dark photons
using the techniques of Worldline Effective Field Theory. We compute the
conservative dynamics up to $1$PN order for gravitational, electromagnetic, and
Proca fields and up to $2$PN order for the scalar field. The effect of
axion-electromagnetic coupling ($g_{a\gamma\gamma}$) arises to the conservative
dynamics at $2.5$PN order and the kinetic mixing constant ($\gamma$) at $1$PN
order. Furthermore, we calculate the radiation due to the various fields
present in our theory. We find that the contribution of $g_{a\gamma\gamma}$ to
the gravitational radiation appears at $N^{(7)}LO$ and to the scalar radiation
appears at $N^{(5)}LO$. We also find that these radiative corrections due to
the coupling $g_{a\gamma\gamma}$ vanishes for any orbit confined to a plane
because of the existence of a binormal like term in effective radiative action
but give rise to non-zero contributions for any orbit that lies in three
dimensions. Last but not the least, $\gamma$ contributes to the gravitational
radiation at $N^{(2)}LO$ and $N^{(4)}LO$.
