I want to use Stack Overflow from my office, where I'm not supposed to use my personal Gmail and Facebook accounts. I've connected my Stack Overflow account to my personal Google account. How am I supposed to log in to Stack Overflow when at work?
According to the section How do I add or remove login credentials from my account? in the Help Centre, you can set up a straight out Stack Exchange login (this is what I do).
On your profile page, go to 'Edit Profile & Settings', select 'My Logins' and click on the button 'add more logins...'
Then follow the instructions laid out in the top How do I change my OpenID provider(s)? answer.