What is the ruling on working for a Jewish or American website (such as oDesk) providing services for money, such as design, advertising, or programming?

The ruling is based on the permissibility of the actions you will undertake. There is no objection to dealing with a website owned by a non-Muslim as long as the work is permissible, as there are accounts of the Companions dealing with Jews, and the Prophet, peace and blessings be upon him, did not disapprove of that. If the website's activity and the services it provides are permissible and do not assist in any wrongdoing, then there is no objection to that, nor to the compensation received for it.