Permissions denied to owner, although it is set to 666 in .ssh directory
Steeldriver is right. On directory you need also x
access flag to be able to list files inside.
Fixing the directory using chmod 700 ~/.ssh
should help you to get into this (correct) state:
$ ls -ld ~/.ssh
drwx------. 2 user user 4096 Aug 26 10:37 /home/user/.ssh
Also you should fix your keys using chmod 600 ~/.ssh/id_rsa
and chmod 644 ~/.ssh/*.pub
to get this:
$ ls -l ~/.ssh/
-rw-------. 1 user user 1766 Mar 7 2014 id_rsa
-rw-r--r--. 1 user user 415 Mar 7 2014 id_rsa.pub