What are the alternatives to HTTP (per
WebSocket). Their corresponding secure variants https and wss included.
From Node.js, you can do pretty much anything. E.g. UDP is directly supported (dgram module which is shipped with node.js), and npm has a plethora of third-party modules for many other protocols, such as SMTP, IMAP, FTP and XMPP; see https://github.com/joyent/node/wiki/Modules for one list. And if you can't find a ready made module for your favorite protocol, you can implement one yourself.
Now when it comes to browsers, you are much more limited. Those you listed are all I know (browser plugins excluded, of course). So you'd need to connect to a proxy server with HTTP(S) or ws(s) and do the actual protocol stuff from there.