Why is it important to hear these characters' voices (Padre Blazon, Boy Staunton) and how do they connect to themes and shed light on...

These characters' "voices" provide a different perspective, for Dunstan, on life in general and his own life.  The two characters are very different from each other, but each of them serve the purpose of helping Dunstan better define himself.

Padre Blazon comes into Dunstan's life as an older, trusted advisor.  What Blazon thinks about Dunstan's life is not necessarily what one would expect from a person of a religious order.  He actually counsels Dunstan to focus less on his compassion and feelings of obligation toward Mrs. Dempster, but to try to figure out what role she plays in his life.  Blazon encourages Dunstan to understand why he feels such obligation towards this woman, and to worry less about her suffering than he does.  Dunstan has, in fact, done everything he could for Mrs. Dempster; more, in fact, than anyone could have asked him to do.  And Blazon is trying to find out why Dunstan feels such obligations, and the woman's psychological purpose in Dunstan's life.  Blazon is more inured to human suffering, perhaps, than Dunstan is.

Boy Staunton, Dunstan's childhood friend and the person much more directly culpable (if anyone really is) for Mrs. Dempster's madness, has a completely different view of life than Dunstan.  Often we get to hear, throughout Boy's life, of his ideas of what is important and meaningful; most of which is in direct oppposition to what Dunstan feels.  Boy is materialistic (in the extreme), a sexual adventurer, and selfish father and husband.  Staunton, in his worldy glory, provides, for Dunstan, someone to always look down upon and to feel superior to.  He also sharpens Dunstan's aceticism through his material excesses.  Surprisingly, the two men remain lifelong friends.

These two strong voices, as distinct from each other as they are from Dunstan, provide counterpoint to Dunstan's telling of the story, and also show us alternate views of Dunstan.  Though Boy is hardly a sympathetic character, he does point out some of Dunstan's less likable qualities.  Blazon shows the reader how Dunstan, even while doing good, has obsessive tendencies.

Not only do these voices point out characteristics in Dunstan, but they illuminate some of the themes of the book as well.  Blazon certainly helps develop the idea of sainthood (which is as much secular as religious in this novel), and also helps Dunstan with the nature of the self (which is perhaps the overriding theme of the novel).  Another theme is the pointlessness of overly worldy existence (as exemplified by Boy Staunton), and, especially, the perils of hubris.