I've stumbled upon this interesting talk by Nathan Willis about FreedomBox and the Tor network. If you've never heard of them, FreedomBox is a community-developed private server system to host web services on your own computer. Tor is the renowned onion routing implementation that aims to improve anonymity when browsing the web.
The speaker describes his personal experience installing and running a FreedomBox installation that is only accessible over Tor. I tried to summarize some points I found personally interesting.
Routing non-web application over Tor
Tor offers torify, a wrapper around torsocks, that lets you proxy the TCP traffic of a given application via SOCKS5 protocol - no UDP though. It is helpful for applications like IRC bouncers, provided that they support the SOCKS5 protocol. At 24:18, Nathan describes how the issues he had trying to "torify" Radicale, a CalDAV application, and some IRC bouncers.
Nathan also describes some issues with using Android applications to access his self-hosted applications over Tor. Tor Browser on Android works in the same way of its desktop parent, so at least he can access the web applications running on his hardware. To proxy the traffic of native Android applications, you can use Orbot - it doesn't always work, though. Nathan also explains some examples of "mobile madness" he found when configuring mobile applications for TT-RSS and Radicale.