Well I cannot give you a complete guide, but this should put you in the right direction.
First off each software will need 2 components, which may already be built in. You need something to create/write the RSS feeds, and something else to read/parse/place the rss feeds.
I have not used PHP-nuke for a while, but the version I had, had a built in module to add rss feeds as blocks on the homepage. It may have been a mod, but I know it existed. You will need this to read the feed from invision.
On the invisions side you will need a hack/mod to create a latest post rss feed. (it may be built in in the current version, if so we do not have it enabled on an invision site I own). Now take the url of this feed put in in the box/module on PHP-nuke and viola your latest posts will be shown there.
For php-nuke you need to create an rss feed of you last articles/news stories. There may be a built in plugin or you might need to find one.
Now depending on where you want to place the feeds on invision you will either need to install a php-rss parser and place them in the template of every page, or if you want it just on the home page you will need to modify your template...or you can make it more of a home page/portal by using a mod/hack vBadvanced. Shoot me a sticky if you want to see a vbadvanced version of invision.