While not specific to WordPress I get this question often because this topic is new for many small churches. But not totally new since most churches have sound systems that have been set up for capturing sermon audio to tape. Though when you start talking about MP3's and sermon podcasting and the like, it gets confusing.
SermonAudio.com, while their sermon audio hosting service is not free, has good articles on capturing audio that I think would be of help to those who are interested in posting their sermon audio to their website:
Once you've got your sermon audio in MP3 format you're ready to post it to your website. If you are using WordPress to power your personal or church site you have powerful tools available to you making it much easier to share your audio. But that will be for another post.