To delete stickies from your Index Card you will have to remove them from the Index Card first.
To empty your Index Card, you will have to drag each individual sticky out of the card and into the main part of your Storm.
Once they are out of the Index Card they can be deleted by clicking the wheel on the top right corner of the sticky and by clicking Delete.
You can also enter the Sub-storm by clicking the three little sticky notes stacked on top of each other and select multiple stickies at once. Either pick Delete or Move To to remove them from the Index Card.