CSS styles for embeded posts andpages

Hi there,
I’m setting styles on a inhouse project. We have linked to pages and posts just by pasting in the link to the page. That in itself works fine and WP makes an embed box [class .wp-embed?] using the styles that are in the file
‘siteroot > wp-includes >embed.php’

However we care alot about our visual identity so I want to style the box, it’s headline, fonts, line-heights – the lot basically. While this is fully doable as soon as there are an update my changes and styles are of course resetted.

Also if I just link to a css file sitting in the theme folder that link will be broken with an update of the file ’embed.php’ .

Is there a way for me to move those styles and templates to the theme directory? Maybe into the functions file? Or is there some other approach to styling the embed boxes?

regards, Per Mattsson