As this is a community and I feel obliged to help, I want to share with you that I had successfully removed the WP_Multilingual plugin. It was a long way 'till I got the blog back working, but I investigated the case.
So, the reason I was unable to see post body (described above) is that they are not physically placed in the correct table. Default WordPress installation expects content to be saved in wp_posts table, column post_content. Installing WP_Multilingual changes the way posts are saved: their new destination is in wp_postmeta table with a different format. So when you remove the plugin, you cannot revert easily because of the absurd database change.
I had to find only the reasonable posts from the wp_postmeta table. Then I got them parsed (most of them manually, because of the different structure that made them really hard for regex). And then updated the post_content column in wp_posts.
Deleting the plugin restored the previous state. I had to refresh the permanent links, too. Also, as they were saved in the DB, I had to change them with an update query with:
SET guid = replace(LTRIM(RTRIM(guid)), '/bg/', '/')
Of course, there were many redirections from outside, with the old /bg/ format links, so I added in .htaccess:
Redirect /blog/bg /blog
That's what made my blog working again.
P.S. I've had another issue on Pingback problem. Removing WP_Multilingual solved that one automatically.