To clean the problem that was not allowing to get logged through wordpress openID, the solution was to get into the wordpress and then I deleted all site URL there:
Dashboard > Settings > OpenID > URL [x].
Delete
When I tried again to login again, it asked me to give the permission, and it worked.
I also noticed that wordpress openID works a little bit better with StackExchange than with StackOverflow. So, I finally managed to get logged with wordpress openID through my StackExchange profile. From my StackExchange dashboard, in [my logins], I included additional options for login, such as google openID. Currently I only use google openID as it seems more stable and is working nicely.