I'll start by assuming that when you say "email ID" you actually mean "email address" which in turn is the user id for those social media networks
is it possible to use the API's of any of these Social Media applications to map the email ID I have to a user in those applications and then to get the user's public information?
Yes and No. In order to request profile information from of these social media networks (let's called them just "providers") your app will need to request it on behalf of the actual user. That is, the user will need to authenticate itself with these providers through your app. For this to happen, the user will need to provide a minimum amount of information (email and password) and your app will need to authenticate as well...usually through OAuth or a native API by specifying an already issued "App ID" (or Client ID) and an App Secret. This is information you should receive by these providers once you have successfully registered your app with them.
is anyone aware of any 3rd party products / API's which can help provide this kind of identification?
I'm not too sure and this is out of the scope of Stackoverflow...but, do you really need to add another abstraction layer in your project? Another dependency? Consider interacting directly with these providers, you have more benefits
So, basically, your app will have to get the user to supply his/her credentials in order to request this information. In the case of OAuth, your app will never see these credentials because the authentication process happens outside your app, all your app will receive is an access token to request the information that is available within the scope of the access token. By that I mean, you have to request specific permissions. There's a lot of information available on the developer's site of these providers and I'm sure you'll get around it without any problems, but feel free to ask if something is not clear enough.