I changed to a new theme (Outline) and my old side menu appears under the navigation dropdown menu. When I delete the code, it just comes back when I publish. I have tried to find the source, so that I can delete it there, but no luck.
Not sure what to do next.
All the links listed above the products are most likely the old per-page links to other pages. Since you are now using the global Navigation, you can remove those.
On a page-by-page basis you would go to Pages > select the page > Assign Items > Page > select all the pages listed in the 'Page links assigned' box > Delete > Save Changes > and Publish.
If you want to remove page links from multiple pages you can go to Pages> select all pages you want to change> Power Edit> under Link Info, add 'Links To Page'> indicate individual edit if required, proceed> you will then be able to Select and edit the page links for each of the pages previously selected> Save Changes> Publish>.