Hi -
It depends on which forum software you're using. Most forum suites have different levels of security/bans to accomplish what you're looking to do.
For example, I'm an admin for a forum (using Invision Power Board 2.0.3) where you must register before you can enter/see any topics, posts, etc.... We have it set up where each registration must be validated by an admin. Using this setting (in your admin config) external sites can link to topics, pictures, etc... all they want, but each time they attempt to enter, it drops them off at the login screen. In your case, each image they're trying to link from your site would show as a broken image.
I suggest you go through your admin controls for your particular suite. You may be able to accomplish your goal by setting up IP bans, link/external reference bans, no index/spiders allowed, no guest viewing or things like that. I haven't seen the "do not allow right click" as an admin-config option within my suite, but I know there are many custom scripts out there that can do it. If your forum allows you to edit the code, I'm sure you could get it in there. However, keep in mind - if you're dealing with security folks they probably know the work-around from the "no right click" as it's pretty easy to bypass.
I'm sure the tools are there - sometimes it can be a challenge finding them in the config area. I know we have about 10 million settings available -- and I'm using about 19 of them.
Good Luck.