Q: How can I delete TextEdit as my default word processing application?

Hmm, not sure how the privileges are set up on your machine...

Here's is another way, assuming you are using ML:

Select the document in Finder, right click (control click) to get the contextual menu, choose Open with. A list of typical apps for the doc type would be visible. Don't choose directly from there-instead click on Other at the end of the list. This will open a Choose Application window; select 'All Applications' in the Enable dropdown, choose OOO and check the 'Always open with' option