[Brian]

Welcome to the forums, siyuan!

If I'm understanding your requests correctly, I think OmniFocus can do what you're after.

For example, OmniFocus supports both "tomorrow" and "tomorrow, 8pm" as due dates. If you do not specify a due time, OmniFocus will use the time specified in the "Data" pane of OmniFocus for Mac's Preferences.

If your device is running iOS 5, OmniFocus will use the Notification Center feature to provide reminders on your device - since the data is already on your phone, the push notification system is not required.

Regarding the "do SAT OG" task - it sounds like you want an action "due every 1 day". The first action would have 3/20/12 as the deadline, and when it was checked off, a new action that was due the following day would be created.

Does that help? If not, let us know and we'll be happy to assist.