In "The Road" Ely says that God doesn't exist and they are his prophets; the father says that his son is God. What do these quotes mean?

In this novel, the characters live in what seems to be a pretty godless existence.  The world is wasted, and human decency is on the road to extinction.  In its place is a form of barbarism that is almost insufferable to think about, much less see with your two eyes as the father and the son do frequently.  They live in the stuff of horror movies.  So, Ely speaks from his heart when he says that God does not exist; to believe in God in such an awful world is difficult indeed.  When he says that "we are his prophets," he is meaning, the people on earth.  It is the people alone who are in charge of preaching about God, and Ely doesn't believe he exists.  So, instead of touting God, Ely speaks for his belief in a lack of God.  It is through people that God works, and it is people that either proclaim God's existence or not.  So, in essence, we really are God's prophets.

When the father says that his son is God, he is not meaning literally.  He is meaning that his son has the power of God in him.  He has the power to make his reality what he wants it to be.  He speaks figuratively of "carrying the fire," which means, carrying human decency and hope within him.  He wants his son to grow up to be a decent, kind, loving human, and to not be marred by the horrific circumstances in which they live.  That fire, that "god-like" ability, is what the father is referring to--his son's capability to restore human kindness back to the earth, in a world that seems bent on destroying it.  I hope that those thoughts helped; good luck!