I don't know which encoder the church uses but I could easily guess that it's expensive to get. Given the kind of work they need to do they may have very high-end hardware and software, possibly beyond what you want to use for a family website.
Depending on what software you use to play church videos on your computer, you may be able to easily look at the "properties" of the video file and find out what encoding parameters were used. Then maybe you could get by with free software like MPEG Streamclip
to do your encoding. The encoding may be a little slow compared to what other, expensive software can do but it's very versatile and if you're not doing a ton of encoding the speed may not be a problem. It also offers "batch" encoding so you could set up several files to encode and then go out for the evening while the computer works.