I was wondering if there is a way to integrate the facebook status update into our website. You know like, if a status is updated in facebook or a post is posted, then I want the same update/post to be posted in our website as well.(saw it in Get Connected section of HOME page of http://www.griffith.edu.au)
Yes it is possible with a bit of knowledge to create a similar feed by using FB developer api https://developers.facebook.com/docs/reference/api/ , or you can just use social plugins and place a like box on your site https://developers.facebook.com/docs/reference/plugins/like-box/ .
Find a free plug-in and put it to work for you. That's the easiest way.
What script you using, so i can give you the plugin, if you using wordpress means, there is lot of plugins for that.
Facebook has official wordpress plugin which has the option for a box where people can see the updates of your FB page. It's very common, actually.