The key to understanding communication between God and humans is the Holy Spirit, the third person of the Trinity. It is an important Christian teaching that those blessed by accepting Jesus into their lives are endowed with the gift of the Holy Spirit, the indwelling power of God in their hearts and minds. This Spirit is the Spirit of Jesus and is the means by which the risen Lord is present in his community and in believers' souls.
The role of the Spirit is to be the moral force that drives the Christian life, animating Christians to goodness and to overcome the weaknesses of their nature, which otherwise would be too much for us to deal with. The Spirit is the means by God communicates with his people, for it is a source of inspiration. Initially given at baptism, it is accessed through prayer and the sacraments, regular performance and reception of which empower the Christian life.
But does the Spirit speak in voices? I am not going to dogmatically say yes or no, but it does not do so in audible voices that can be heard by the public, and most who "hear" voices agree that they are not uttered by any physical, bodily source. But it is clear that many Christians believe that the Spirit speaks to them, delivering messages about their lives and God's direction and will for them. But what I think is happening is not that an audible voice is heard, but that God through the Spirit inspires ideas in the minds of the recipient. These are what the philosopher Descartes might class as adventitious ideas, ideas that come to you from outside. But humans are creatures who think in language and so even though these ideas are not uttered in any human language, the human mind linguistically expresses them in a language that it can understand. I am aware that there are people who talk in tongues, but this is a phenomenon that baffles me and for which I cannot give an explanation. Thus I expect that if God wants me or anyone else for that matter to receive a communication He will inspire me with ideas, but my brain will render them in English.
It is also important to say that for many Christians God communicates through the medium of rituals, works of art and music. Here you cannot separate the medium from the message. A person listening to the beauties of Gregorian chant, Catholic ritual music, may feel that the melody is a vehicle through which the influence of God shines. You may also feel that God's communication is often experienced through the profundity of silence, which is as much a medium as art is.
Thus Joy Behar's supposed joke about the vice president's sanity is not only offensive, but reflects a limited and unsophisticated understanding of Christian thought and religious experience