Is there a way to get a user’s email ID after verifying his/her Twitter identity using OAuth?

The user’s email address can not be retrieved via the API. This is a deliberate design decision by the API team.

UPDATE 2015.08.18:

It is possible to request an email address from users, but it requires your app to be whitelisted. See https://dev.twitter.com/rest/reference/get/account/verify_credentials for details of the API call and this form to request whitelisting of your app.