In general, OAuth is doing two things. First, it's a way of leveraging the authentication mechanism of some other site (e.g. Google, Twitter, Facebook) for your site -- in effect, you're saying that if they have an account they can log into on the other site(s), you're willing to rely on that for their authentication to your site (that is, they don't need to register & set up a separate name/password on your site). When you use this authentication mechanism, the user is literally redirected to the other site to enter their credentials (you never see those; just the fact that they authenticated successfully); AND as part of this process, they need to explicitly agree to that site reveal certain information to your application. At minimum, the fact that they have an account.
That leads to the second part. Depending on the provider, they may reveal nothing more. Or, they may be given the option to authorize your application to access additional information on their behalf from that site -- for example (as you mention), their social graph. As part of your OAuth request, you can indicate what such additional information you're requesting access to; but this will (or should) always be made explicit to the user, and they always have the option to decline (or to revoke this access later).
What I'm getting from your last response is that there's information about your users you want to access via Google APIs, as well as Facebook, Twitter, etc. My recommendation, as several others have suggested, is that you determine what is the *minimum* necessary for users to use your site at all, and only require that for initial sign-up; and then give users the ability to gain additional capabilities (by way of giving auth via OAuth to other sites/services), as on option.