Show, don't tell
Frankly, I doubt you'll be able to convince them solely through presenting a case for or against a particular way of doing things, especially given the response you've already received (which suggests that they may not be open to a logical argument).
Instead, just start implementing best practices as you go. You'll have to deal with the table layouts for existing pages, but new pages (and better yet, projects, if your company does projects) provide you with a chance to convert to a div-based layout. For existing pages, you can move all of the inline styles to stylesheets and clean up the HTML as you go along.
Additionally, prepare responses for the questions you'll likely receive for making such changes. Here are some ideas:
Q. Why did you remove all of the styles from the HTML?
A. I moved them to an external style sheet so that styles can be reused and so that we can leverage the cascading nature of CSS. This will allow us to reduce file sizes, which not only increases download speed, but also makes maintaining the pages easier and faster. It will also allow us to leverage browser caching, because external stylesheets get cached and, therefore, only downloaded once.
Q. Why did you use
divs for layout?
A. The W3C specifies semantic meanings for elements, and tables have a semantic meaning as tabular data. My migrating to
divs, we can reserve tables for tabular data, making them more meaningful, especially to visitors that aren't using visual browsers (including screen readers, and search engine spiders). It will also help SEO, because search engine spiders may not see a table-based layout as primary page content.
Q. Why did you move the JS?