Do you want these in one long list like regular archives only sectioned?
The way I see it you may have one of two situations to consider.
1. You either have a few hundred posts and at 20 or so per page, you may not really have a situation where there would be multiple categories of posts on one page.(If that makes sense.)
2. The other situation is that you have only a few posts in each category and really only need to show 4-6 posts from each. In which case, they can be separated by category for easy viewing and allow you to title each section accordingly.
In the first case, you might be better off just creating archive pages such as category-articles.php, category-News.php, etc. Just copy your archive template but title the file accordingly. (There are other ways to do this as well.)
In the second case, you can have multiple loops on a page. If you are a coder these tuts may help:
For one long list as a regular Archive you can also use orderby=parent in those query_posts.