I have a document in Word 2010 that uses multi-level outlined numbering. Is there a way to make all odd numbers and the associated text one colour and all even numbers + text another? Thanks for your help

First, do not depend on the little button to insert your numbering. Instead follow the instructions at How to create numbered headings or outline numbering in Word 2007 and Word 2010.

Second, in answer to your question, I know of no way to do this.

Are you using multilevel numbering? Or, is it a list? Is it just one level you want to have this happen with?

It may be possible to do something with Styles and setting the style for the following paragraph. It would be a lot of work to set up and possibly to maintain. Are you willing to devote 100 hours to this project?