I added these lines to hosts file and now some images (mostly i.stack.imgur.com urls) are visible. Actually, I viewed dozens of questions and can see images without any problem. It shouldn't be that simple.
To give an idea of the extent of this problem: according to this stackexchange.com search, over 8000 posts are affected. Some of them may contain images which are already lost (e.g. the last image in the Meta.SE post you found).
There are some options:
Edit the post and upload the images via the Stack Exchange image uploader, which stores them on imgur.com....