Handling interference is one of the main challenges in the design of wireless networks. One of the key approaches to interference management is node cooperation, which can be classified into two main types: relaying and feedback. In this work we consider simultaneous application of both cooperation types in the presence of interference. We obtain exact characterization of the capacity regions for Rayleigh fading and phase fading interference channels with a relay and with feedback links, in the strong and very strong interference regimes. Two feedback configurations are considered. In the first configuration there are feedback links from both receivers to the relay, and in the second configuration there are feedback links from both receivers to the relay and to their opposite transmitters.