It would be legal to stream them WITH correct permissions in place. Download, not at all. You should look into broadcast licenses or streaming licenses I think they're called...can't remember, but there is a great thread on this very topic somewhere on the forums, you should be able to find with a little searching.
Most churches that I know simply edit out the music portion of their service (unless they're using original music) and offer the messages as their podcast.
Associate Director of Worship & Media at St. Simons Community Church .He is also the content curator and editor here at The Worship Community.