This looks like disk page corruption. In such a case, the very first thing you do — aside from verifying that your backups, replication, and WAL archiving are

This looks like disk page corruption. In such a case, the very first thing you do — aside from verifying that your backups, replication, and WAL archiving are all working — before you even try diagnosing your problem any further than "something weird is happening" is make a filesystem-level copy of your PostgreSQL cluster. (If you're running LVM, ZFS, a SAN, or any other thing that lets you take an instantaneous filesystem snapshot, so much the better. Do that, and then copy it.) Then, and only then, should you even contemplate trying to un-fuck your database. I cannot stress this point enough. That means make a tarball, or cp the directory, or rsync it, or whatever disk file level tool you prefer, and specifically and emphatically not pg_dump. (It's probably not going to make things any worse, but if you do have corrupted disk pages, pg_dump isn't likely work, anyway.) Flailing around trying to fix things can sometimes make them worse. If you're working on your already broken data, and break it further without the safety net of a fs-level backup, you're ... well, you're worse off than you were five minutes prior, aren't you?