After years of using screen+irssi or tux+weechat, I finally found a GUI app that provides the same functionality. Quassel IRC. It is a combo IRC client and BNC server that is built to tightly integrate with each other. No more re-attaching to screen sessions or struggling with BNCs behaving rationally.
There are two components. The client and core. The core provides the relay functionality and the client is just that. Setup the core service on your server that you have been using for screen or BNC. Just start the process. Then you connect with the client. The first connection you establish an administrative user account and start building your IRC networks.
Once you are all setup, install the client on your other devices, Linux/Win/OSX/Android (sorry, no iOS yet), and connect it to the core. Everything you do on any of the clients is automagically sent to all connected clients. All of your joined channels are there, all/most of your preferences transfer over, all using the same nick/connection to the IRC network. One of the coolest features is the automatic scroll back. If you open a new client, it will automatically pulling n number of scrollback and if want to read earlier than that, once you hit the end, it will pull some more!
If you are an IRC’r that has wanted a GUI but not wanted to give up the benefits of screen, check out Quassel.