I also use weechat (on cygwin since they don't have native windows builds) + glowing bear. It's great as long as you're at a PC, but it's missing a way to get notifications (for example when you receive a /msg or /notice) when you're away from the PC but have your mobile with you.

Yeah, that's hard to implement without a central server component or annoying setup. I use IrssiNotifier (despite the name, it also works with WeeChat). It's not great but I get push notifications for highlights on my phone.

Yeah, it would have to be a push notification. Running an actual IRC client that had to maintain connection on mobile would destroy your battery.

Anyone aware of anything that works on mobile that does this?

Well irssinotifier uses Google cloud messaging (is that the current name? The Google push service). It encrypts messages on the server and decrypts them in the client, using a passphrase. It's a technically neat solution but a bit annoying to set up.

It has a script for weechat (and of course irssi), not sure about other clients.

Or you can use pushbullet /..., there should be scripts for any popular scriptable client

For quassel there seem to be options: https://news.ycombinator.com/item?id=12065792

+1 for Glowing Bear. I haven't been on for anywhere near 6 months but I know I will be eventually.