You can manage which availabilities customer's are allowed to order by doing the following:

1. In AE admin, go to Settings>>Sites>>click the site you'd like to manage.
2. Under the Cart tab, find the "Allow Ordering of" label which will show a list of availability checkboxes.  Check the availabilities you'd like to ALLOW ordering for; Uncheck the availabilities you don't want users to order.
3. Once you're done, click Save Changes.

The most common setup for our clients is to check "In Stock" and "Low Stock", thus allowing your customers to order anything that has a stock qty greater than 0.