It is odd to me that there are tasks due today that are not being processes and tasks due in several days that are running. A good feature would be to prioritize tasks that are due sooner than the ones due in several days.

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Which task runs also depends on your resource share priority between projects and if the time run of each project is matching that resource share allocation. If you are running a project at 100% and you add another project at 100%, BOINC MGR will play catch up and run the new project much more often until the resource share evens out. Tasks from the old project may sit there until their deadline in this case.

This is assuming there is nothing else preventing tasks from running like being out of memory, etc.