Because of the connected nature of information in Headrush, deleting things can cause unintended consequences or deleting information you didn't expect to delete. Therefore you'll find restrictions on deleting both tasks and modules.
You can only delete modules that are in have a status of 'Draft'
Set module status to Draft
Choose the Overview tab
Scroll to bottom
Click Delete Module (this will only appear if module is in Draft)
You can only delete tasks that have no evidence
Open the task from the Task Board
If there is no evidence, you will find a "Delete this Task" in the menu at the top of each task: