Yes, you can place the same SquareOff in multiple locations. This is always helpful as SquareOffs become more interesting as the activity snowballs. For example, a question with 3,000 votes and 75 comments is a lot more interesting and will keep each new reader on site longer than a question with 200 votes and 5 comments.
Including the question in multiple articles is super easy. After creating a SquareOff, just paste the same code below wherever you'd like. Example:
We also provide the polls page Feeds option to act as an archive for all questions that have been created.
Example - KTVZ.com creates one question per day for a top article. This same question is displayed within that article, featured on the home page (using a small Feeds embed), and on the polls page (using a large Feeds embed).
Polls page (w/ the same SquareOff): https://www.ktvz.com/polls?soid=14107
Home page (half way down the page on the right): https://www.ktvz.com/?soid=14107
(The "soid" in the url is simply included in social shares, etc. to load that particular SquareOff first for the reader.)