How to control my device from HTTP?
GTalkSMS is worth a look (not HTTP but does also what you want, even easier accessible).

It's an open source XMPP bot (google code project) that you can add to your Google Talk friends list or communicate to with any XMPP client.

You need to find a suitable commandline/scriptable XMPP client for your solution yourself however (as the 'curl' replacement in your question), not sure what you like to use.

Here's an excerpt from the feature wiki on its Google Code project page:  


  Further Commands
  send and receive files to/from the phone: "send", "ls"
  enable disable bluetooth: "bluetooth"
  [...]
  take a photo and send it via XMPP: "photo"
  [...]
  geolocalize your phone - it will send you google maps links: "where"
  [...]
  get help, using "help:all"