How to save attachments against an event and task (Activities) in Salesforce?
Its only possible in edit mode (after created the event/task and the click the edit button).
If users are allowed to add attachments to tasks and events (Activities), they must edit the task or event in order to display the ‘Attach File’ button in the Attachments related list. The ‘Attach File’ button does not display in the Attachments related list when only viewing a task or event.
Please see https://help.salesforce.com/HTViewSolution?id=000006460&language=en_US.
Various Salesforce.com customers have observed that this is inconsistent with the way attachments are added elsewhere, but SFDC do not give a reason.
So after created the event or task then in the detail page just click the Edit button and then add attachments. (see the below screenshot)