I store aliases (+ info about the service I provided them to) in the database and use simple PHP script to manipulate the db from the web.
On the mail server side, I have postfix set up to read the database and deliver everything for a valid address to a single mailbox.
It should be workable with any service that will allow you to setup aliases for a single mailbox. If they allow to set it using API, that would allow for automation.
On the sending side, given that I haven't yet found a need to communicate too frequently with any of the services I use via email, I have a simple PHP form to send email with the specified alias address set as From on the envelope and inside the email.