Hi There
It sounds like your old URLs have not been 301 Redirected to the new URLs. If so, it's now a case of damage limitation.
As a matter of urgency, you'll need to map your old pages to point to the most appropriate new ones, then 301 redirect those old URLs to the mapped new ones.
Then update your sitemap.xml and submit/re-submit it via Google Webmaster Tools (GWMT). Also ensure that your robots.txt file is up-to-date.
If it's not too late, which it probably isn't yet as you say that Google is showing your old URLs, this will ensure that as much page strength as possible is retained, by being transferred from the old page to the new one via a 301 redirect. It will let Google know which old pages to replace (reindex) with the correct new page.
This will also reduce the number of 404 pages that are presented to your visitors as the search results (old URLs) will be redirected to the correct new pages.
As for your homepage, hopefully that hasn't changed (as in a new domain name). If it is indeed the same as before, you'll still get visitors finding that page correctly. Though with the site showing so many 404 pages and at present, old pages loosing strength as they cannot be found, your domain authority and homepage strength could start to reduce soon, thus reducing your rankings for your homepage.
If your domain name has changed, you'll need to inform Google of the change via GWMT.
If the above isn't done and done soon, your old pages will start to disappear from search engine indexes and you'll be starting from scratch with your new pages.
Hope that helps,
Regards
Simon