What is the relationship between theme and style in prose fiction?

There doesn't have to be any relationship between theme and style at all. Theme is what the message of the work is; style is how it is done. For example:

Here lies the body of Micheal O'Day

Who died defending his right-of-way

His right was clear, his will was strong

And he's just as dead as if he'd been wrong.

38-40As they continued their travel, Jesus entered a village. A woman by the name of Martha welcomed him and made him feel quite at home. She had a sister, Mary, who sat before the Master, hanging on every Word he said. But Martha was pulled away by all she had to do in the kitchen. Later, she stepped in, interrupting them. "Master, don't you care that my sister has abandoned the kitchen to me? Tell her to lend me a hand."

41-42The Master said, "Martha, dear Martha, you're fussing far too much and getting yourself worked up over nothing. One thing only is essential, and Mary has chosen it-it's the main course, and won't be taken from her."

both these exerts have the same theme (there are some things that are more important than others) but are told in entirely different styles.