Mannered, Biblical
Wilde, who is usually a pretty hilarious dude, isn't as witty here as you might expect. There's not a lot of wordplay on display. This has a lot to do with the tone and genre of the piece (You can check out "Genre" and "Tone" for more on that.) Wilde's characters speak, well, "biblically." What does that mean, you ask? Well, the Bible in question would be the 1611 King James Version translation (often referred to as the KJV). So it makes sense to start there. Take a look at the beginning of Matthew's account of the Salomé story, as rendered in the KJV:
At that time Herod the tetrarch heard of the fame of Jesus, And said unto his servants, This is John the Baptist; he is risen from the dead; and therefore mighty works do shew forth themselves in him. For Herod had laid hold on John, and bound him, and put him in prison for Herodias' sake, his brother Philip's wife. For John said unto him, It is not lawful for thee to have her. (Matt 14:1-4)
See all those "unto"s and "thee"s? Wilde's dialogue is sprinkled with them, especially when it comes time for Jokanaan to speak. "When he cometh," he cries out toward the beginning of the play, "the solitary places shall be glad. They shall blossom like a rose" (36). This is some heavy stuff, and, for the most part, Wilde doesn't mess around.
But on the other hand, it would be pretty twisted to make this play into a comedy. That kind of dark humor wouldn't be around for almost another hundred years.