How can I use Python from a sketch?
It looks like from that page you can also use various API's to execute
  Python directly on the Arduino.


I don't see that, at all. All those links show you how to communicate with the Arduino over serial using Python on the host side.

You'd need a python interpreter to be able to run python on the Arduino. There is the Python On A Chip project and it seems like they have support for the Mega.


  2010/09/01 (1bdb8d31f27b) New platform: Arduino Mega.


Some more info from the PyMite page:


  any device in the AtMega family which meets these requirements: 20KiB
  Flash and 4K RAM, will run today


I doubt you'll find anything that'll let you mix Arduino and Python code in the same sketch.