Chris, this has nothing to do with Moodle, but web server configuration.
if you are on CPanel, then you'll find option of HOTLINK PROTECTION in CPanel, just mention your domains and the file extensions.
in case you are not, then type the following command in your .htaccess file
RewriteCond %{HTTP_REFERER} !^http://mymoodle.com/.*$ [NC]
RewriteCond %{HTTP_REFERER} !^http://mymoodle.com$ [NC]
RewriteCond %{HTTP_REFERER} !^http://www.mymoodle.com/.*$ [NC]
RewriteCond %{HTTP_REFERER} !^http://www.mymoodle.com$ [NC]
RewriteRule .*\.(jpg|jpeg|gif|png|bmp)$ - [F,NC]
replacing mymoodle.com with your URLs, and in last line you can mention the file extensions like MP4, FLV etc (just the way I mentioned jpg|jpeg etc.)
and if you want to redirect users to some other page, that tries to open the link directly into browser you can mention in last line
RewriteRule .*\.(jpg|jpeg|gif|png|bmp)$ dontnotcopy.com [R,NC]
where you can replace the "donotcopy.com" with the path to some HTML file or image (showing finger or something)
Also, just to add, you cannot fully stop people stealing content, as though this is one way to prevent linking content to outside, still there are ways, like people using IDM (Internet Download Manager) and Maxthon Cloud Browser, they do get the links no matter you have initiated HotLink Protection, though I am working on solutions to get rid of this issue of videos being stolen, but not easy task this is. One other way is to send ABR (Adaptive Bit Rate) chunks to the users, this way many other downloading clients wont be able to get file intact, for that you have to have a streaming server intact.