how to load new posts with ajax

The effect is called infinite scroll and you can find some themes and plugins to do it.

I have not used it before so can’t vouch for it but you can try http://wordpress.org/extend/plugins/infinite-scroll/

So if someone is sitting on your website and you publish a new post you want it to automatically appear twitter style? Is that what you are after?

Got me.

Never seen a plugin that can do that and just did a quick search and came up short.

Good luck!