How to use IRC at school?

Maybe a web based client made it past their web filter. There's a lot of them out there.

A long time ago I used something like sockd to run a local proxy and then send that data to my personal remote proxy server over port 80, something like https://win2socks.com/ I think

Maybe there’s something better than socks these days.

Back then it worked pretty well, but I don’t think they were doing DPI. They (admin guys) did seem to notice large file transfers and seemed to be killing them manually.

I would assume most places these days will collect net flow data at least, so while https will protect the contents, they will be able to see the potentially unusual amount of data moving back and forth to your proxies IP.

I would suggest at least using a VPS to hide your schools IP address from the irc servers. And you may be in serious trouble if you get caught. If you’re in the UK you’re going to be risking jail time, and speaking from personal experience, they take this shit seriously.

So maybe just set up a personal hotspot.

use a web irc client

Yes, use a proxy. Usually 443 is not blocked either, so an SSL encrypted solution is hard to block

There's a few WebSocket solutions out there. Basically looks like a normal HTTPS connection to something that uses a WebSocket, so unless they're decoding TLS and the HTTP session and somehow recognizes that this is a VPN and block it, it'll likely go through.

It's not unheard of for the usual IRC ports to be blocked because it used to be used for botnets. Some servers may have different ports.

Just use a VPN. Proton VPN is a privacy-respecting and trustworthy provider with a pretty neat free plan, I used it for IRC many times, works very well. They have clients for pretty much every platform including Linux of course.