Sorry, but the only way to keep your profile completely inaccessible to these people is to not message them. You might be able to hide your friends from them, but you're right -- they will have access to your profile pictures. They'll be able to see only *some* of your profile though -- not the whole thing. They'll only be able to see your Basic Info and Work/Education Info.
You can try to edit your Friends, Basic Info, and Education/Work Info on your Profile Privacy Settings:
http://www.facebook.com/home.php?#/priva…
On the drop-down menus, check click "Only Friends." Then scroll to the bottom of the page and click the blue Save Changes button. I don't know if this will necessarily prevent non-friends from seeing these aspects of your profile, but you can try. Otherwise, sorry, non-friends will always have access to your profile pictures, friends, basic, and education/work info whenever you message them.