I think it's been implied before, but I'd like to say this and I should have mentioned this earlier. I'm not sure if you already went through this thought process or anything, but hey, it helps ~
You're showing osu! to a bunch of classmates and a teacher who, generally, don't have as much video game intuitiveness as you do. Therefore, you should present the things that can easily wow kids into thinking that it's a very cool or neat game. As mentioned in previous posts, they aren't interested in specific terms, famous maps, momentous events and milestones, or any of that specific community stuff. They want to know what the game is about and what would interest them about it.
It's like you're a salesperson trying to give a pitch on how osu! is a great game to play. With that, you should probably mention the main features, give demonstrations (by demonstrations, videos can work). Since you have Taiko, CTB, and various screenshots of mods covered, I'm thinking you're on the right track though ~ Just make sure you can keep the class's and moreover the teacher's interest in the presentation.
I think online access is only blocked at school? O_o The game client should be fine... You can just take osu! on a USB, play offline, and heck, you can show live demonstrations of the game to your class. This depends on the technology of the computer and projector though... For instance, if the computer is some ancient, sad panda that lacks the needed components to run osu!, then a live demo won't be possible. For that alternative, videos are a godsend, yeah~?