I want to remind task owner (through e-mail) 2 days before a task is due.
I want to send them another e-mail when the task becomes due (on due date).
Finally I want to send them yet another e-mail if task is overdue by more than 2 days.

Workflow rules on tasks do NOT allow creation of e-mail alerts.

How do I do this?

Salesforce has "Reminder popups" - but this works only if the user logs into the app!