All tasks that are both assigned to you and have a set due date will sync to a Streak calendar in your Google Calendar.
You can view all Streak events by navigating to Google Calendar and using that calendar to see all Tasks within a time period, or see a list of all tasks using Google Calendar's agenda view.
To add a due date to your task:
Open the Tasks popup menu
Ensure that your task is assigned to you or a colleague
Select the clock icon next to the task to open the calendar schedule
Give the task a due date.
The task will then sync over to Google Calendar.
This sync is a one-way push from Streak into your Calendar. Changes made to your tasks from within Streak will update in Google Calendar, but changes made from your Calendar will not sync back with your Tasks in Streak.