Note: This plugin currently only supports YouTube videos and MP3 files, but additional formats could certainly be added.
This plugin provides a “Sermons” post type that can be used to share video and audio sermons. When a sermon post is viewed, the video and audio are displayed in a user-friendly, tabbed format for “Video,” “Audio,” and “Download” (which allows the download of MP3 sermons).
It also provides a podcast RSS feed with an options page for various settings for the podcast.
This currently does exactly what I need it to do, but I am very much open to suggestions and (especially) contributions by others who would like to expand it.
Bonus
If you also install the BLB ScriptTagger plugin, it can convert your Bible passages into hyperlinks that display that passage in a pop-up window when you hover over them with your mouse.