We propose a generalized system of nonequilibrium cavity QED with interacting dipoles coupled to a single-mode of an electromagnetic field in strong-, ultrastrong-, and deep-strong-coupling regimes. To illustrate the applicability of the system, an extended Dicke model is developed for atoms undergoing Raman transitions between the ground states in the presence of laser fields and considering dipole-dipole interactions; the latter has been neglected in many previous works. We have studied the effect of a ferroelectric and an antiferroelectric arrangement on the phase transition for both a finite and an infinite number of dipoles. An additional superradiant phase is observed in the deep-strong-coupling regime due to influence of the dipole-dipole interaction term. A high degree of dipole-dipole entanglement occurs for the antiferroelectric arrangement in the deep-strong regime, whereas it gets disentangled quite rapidly for the ferroelectric arrangement. A sharp transition of system parameters is observed in the ultrastrong-coupling regime and beyond. The dipole-dipole interaction also influences the spectra of the system, inducing a significant shift in the peaks, and modifies the average number of photons emitted.