  We consider a mean-field system of path-dependent stochastic interacting
diffusions in random media over a finite time window. The interaction term is
given as a function of the empirical measure and is allowed to be non-linear
and path dependent. We prove that the sequence of empirical measures of the
full trajectories satisfies a large deviation principle with explicit rate
function. The minimizer of the rate function is characterized as the
path-dependent McKean-Vlasov diffusion associated to the system. As corollary,
we obtain a strong law of large numbers for the sequence of empirical measures.
The proof is based on a decoupling technique by associating to the system a
convenient family of product measures. To illustrate, we apply our results for
the delayed stochastic Kuramoto model and for a SDE version of
Galves-L\"ocherbach model.
