Similar to the setup of Squid for HTTP proxy: https://gist.github.com/gmeeker/5e9af73fcf213c67cd86794f506520e6
OpenWRT can be used for SOCKS proxy as well using Dante. No custom builds are required, but some configuration files are currently missing.
opkg install sockd
Based on OpenWRT: 18.06.1
(Note: using tinyproxy might accomplish this with less work, but only 1.10 supports authentication. As of December 2018, OpenWRT does not include that version. However, squid also supports other authentication methods so this guide may remain useful.)
I wanted to turn an ordinary WiFi router into an HTTP proxy, but it turns out that the guides I found are for transparent proxies, and worse, OpenWRT doesn't compile authentication into squid!
Official OpenWRT guide to Squid (don't follow these steps blindly, as its only purpose is HTTP caching):