These selective reminders are not provided in Omnifocus. I only use the due date for tasks that I want to be reminded of with sound. For scheduling all other tasks I use tags (today, monday tuesday, … , next week …, march, april …, next year …).
In the Inspector pane, you can define additional notifications on individual tasks, either ‘before due’ (unfortunately the available durations only go up to 6 hours) or ‘custom’ with a fixed date and time.