Erase Data on my stolen phone without password
It's sad you learned a lesson the hard way.

Because the phone had no passcode, the thief (or anyone else who happens upon it) can see contacts, photos etc. When you get a new phone, it is highly advised that you add a passcode. The time and inconvenience of unlocking when you use the phone is worth the security. 

As for the stolen device, It is recommended that you should at least change your Apple ID password.  Instructions can be found here at Apple Support.  I is unlikely that the thief will guess your old password, but if the current password is weak or can be easily guessed (or worse, you have it plain to see in the Notes app) he could do even more damage to your personal data.  If you have any other Apple device that uses your Apple ID this could be a serious problem.  He could even purchase apps at your expense, change the password himself and lock you out.

If you are still concerned and you have your original proof of purchase, a call to Apple Support may be an option.