SSH into a remote server; but the organization has blocked port 22

You need a reverse tunnel.

From your mac you ssh to your linux VPS, creating a reverse tunnel.

ssh -R *:6667:127.0.0.1:6667 tristan@linux

That connects from your mac-mini to your linux VPS. It makes ssh listen on all interfaces (*) on port 6667. Any traffic it finds (on port 6667 of your VPS) it sucks down the tunnel and punts back into the localhost on your mac-mini (127.0.0.1) onto port 6667.

You can also use,

ssh -f -N -R *:6667:127.0.0.1:6667 tristan@linux

so that you don't see a terminal session (-f backgrounds ssh after asking for your password, and the -N stops it running a remote command). To close the tunnel you'll need to find the process on your mac and kill it.

DCC operations won't work properly, but IRC might.

Caveat: I do not know if this will work for more than one IRC user connection

Note: Depending on why you've been told you can't run an IRC Daemon on your VPS, this technique might be an issue as well (i.e. if port 6667 is blocked inbound to your VPS).

On the VPS, you need to ensure GatewayPorts is enabled in the sshd_config file (usually /etc/ssh/sshd_config).

That's a tricky thing to get done. Your best bet is to use some SOCKS redirector like socksify or redsocks, but none will give you what a VPN can, so you'd better set it up. VPN allows you to connect even whole networks, forward your traffic through secure channels, make your computers all appear as in one LAN and so on.

You can use OpenVPN to do that - there's a pretty good documentation on it's site, though it might require some knowledge about networking to decide what and how you want.

However, if you don't wish to use it, but want to stay with SSH instead - you may refer to SSH-BASED VIRTUAL PRIVATE NETWORKS section of man ssh or https://help.ubuntu.com/community/SSH_VPN, which describes the topic pretty well.