My petition for an O-1 visa was approved whilst in the USA on another visa. I have not yet left the USA to return to my home country to get it put into my passport and do the interview etc. I have a flight to a different country in Asia (not my home country), which would mean I would be returning to the USA without having stamped my new visa. Can I enter the USA on a tourist visa for the sole purpose of changing onto a plane to my home country in order to activate my visa? Or will I be refused entry to the USA as I have not activated my new visa yet?
Not sure exactly what you mean by activation. Assuming you have already received the visa, you simply need to leave the United States for at least 24 hours. Then you can come back in under the new visa.
Also, depending on your nationality, you may qualify for a transit visa waiver. See http://travel.state.gov/content/visas/english/other/transit.html for more information about that.