Lord of the memes

You're right that it does lack the luxuries that makes discord better, especially video clip and picture sharing in channels.
There were ways to set up something called an IRC bouncer, which acted like a middle layer or puppet between you and IRC network allowing that to receive messages and the like while you were physically offline.
And for everything else you'd just send the files directly to whoever you wanted to share it with. Cumbersome, not to mention the pain port forwarding used to be.
Regarding screen sharing, back when IRC was king, the bandwidth wasn't even really there for that. I guess one would use a VNC server/client or some other remote desktop application if that was needed.