Such as winblows networking. This is information you never want the public to see. And it is possible to grab from someone else, if they have gapping security holes like port 139.
You're probably mixing up MAC addresses and NetBIOS names, these are two completely different things
About the original question: that's not possible at all; even if all the clients and the IRC server are on the same subnet as you, then packet sniffers like tcpdump would only see the MAC address of the IRC server's NIC, not of any of the clients - afterall you're only directly receiving data from the IRC server, not from the clients.
I'm afraid there's also no other way to identify users that can change their nick, username and IP (I suppose that's what you're after). You'll have to wait till IPv6 is being widely used, IPv6 is said to make dynamic IP assignment unnecessary. But that's still pretty much future talk