The primary points the wall spaces should be closed off is at the basement or crawlspace level, and the attic. If these areas are readily accessible, sealing them off isn't too hard of a job. They can be closed with plywood, cement board, or even sheetmetal. There's likely to be a few places where wiring or pipes travel in these spaces, so some closures need to be made to fit around those items.
What is below your 1st floor; basement or crawl, and if it's basement, is it already finished where the bottom of the floor is not accessible?