Why don't you enable perspectives by visiting this page (from your iPad!):
http://people.omnigroup.com/kc/Debug...spectives.html
and clicking the Enable Built-in Perspectives link. Then try out the Due perspective and see if that gives you what you need in terms of a display of due items in chronological order.
OmniFocus doesn't blithely reorder items for you, because it assumes that the ordering is significant. If your projects are simply catch-all collections of tasks that can be done in arbitrary order, then it may not matter if they get done out of order, but it certainly isn't the case that all projects fall into that class! However, if you are a due-date driven worker, working from that Due perspective ought to get your independent tasks done in the right order without any need to rearrange them.
I've been using OmniFocus intensively for several years, and the number of times that I've needed to rearrange actions by due date I could probably count on the fingers of one hand, with fingers left over :-) OmniFocus will show the actions in due date order (as suggested above), so if the sequence doesn't matter, only getting the work done by the due dates, I'm going to suggest this is an issue that matters mostly in theory, not in practice.
To reorder the project list, go to the home screen of the application, tap the ">" to the right of the Projects label in the sidebar. Now tap the Edit button. At this point you can drag actions or projects around with the drag handles (three horizontal lines at the right end of a row), or delete them by using the - in a red circle at the left end of the row. Tap the Done button when you are done.
One more thing: if you decide within 30 days of purchase that it isn't going to work out for you, Omni offers refunds!