Can a person restore an iPhone even if it's been deactivated?

My phone has been stolen recently, and we called our phone company to deactivate it. I didn't have the Find My iPhone app installed or iCloud. I was logged into Twitter, Facebook, email as well. But I changed the passwords right away. I know I know. I'm stupid. I already feel freaked out enough.
What EXACTLY happens when you deactivate it? I heard it's still on when you deactivate it and you are still able to use it, just not calling/texting. Can they still go on the internet if it's connected to a Wi-Fi, or use the phone at all, in any way? Can they restore it and use it as a phone? What are they allowed to do on the phone? Please please help me.

If your telephone is stolen, notify your service provider and give them both your mobile phone number and IMEI number.
You can prevent a thief from using your mobile phone subscription just by calling your phone company and telling them you lost your phone. If you have a SIM in your phone, you can also lock your phone. Your phone will require the SIM PIN code regularly to prevent fraudulent use. The SIM will block any service if the PIN is wrongly entered three times.
If your phone has a SIM, you can also prevent the thief from using your stolen phone with his own SIM. To do this though you need to know your phone's unique identification number, called the IMEI (International Mobile Equipment Identity). If you can also give this number to your phone company, they can block the handset from being used with a different SIM.
You can apply some anti-theft app like iKeymonitor on your iPhone which can nearly record all the activities and increase the possibility of finding it back.
Hope it helps.