I use Apache on my machine to share some files over office network.
How can I host them over torrent instead of sending them over http?
There is no such thing as a torrent server - you can create a torrent using your torrent client, add a tracker to improve reliability and then share it. You could probably use the apache server as a webseed - but you're trying not to use the web server, right?
In this specific case though, the speeds you get over the office network are likely to be faster than using torrents - you MIGHT be able to use a local tracker, and have it serve out local IP addresses, but its still not going to be very efficient. torrents are designed for anonymous, high reliability sharing at decent speeds - regular file sharing over lan might end up being faster.
If you want it really fast.. nothing beats good ol sneakernet