Imagine this:
You have a bot in your channel that accepts an "upload-image" command followed by a base64-encoded string representing an image (or a series of these commands if line-lenght is limited, I'm not sure about this part of the IRC protocol). The bot checks that the image is actually an image (to avoid weird injection tricks), saves it on the server and returns a link you can share or sends the link directly to the user/channel of your choosing.
This can be automated with a irc client, of course. Users using old clients will receive an actual link, users of this supposed new client see a clickable preview of the actual image inline.