GetStringValue is en extension method defined on Google.Apis.Util.Utilities.
Similar VB.NET code to this worked for me on VS2012 with the latest version of the library. You can find my VB.NET sample in https://codereview.appspot.com/7007048/, but it still wasn't approved, so be careful using it.
In the samples repository (http://code.google.com/p/google-api-dotnet-client/source/browse/?repo=samples#hg%2FDiscovery.VB.ListAPIs), there is currently only one VB.NET sample, but hopefully the sample above will be approved soon and it will be added to the repository.
Please elaborate more on the references that you have in your project and the stack trace. It looks like there is another overloading to this GetStringValue somewhere else (http://msdn.microsoft.com/en-us/library/2hx4ayzs(v=vs.80).aspx) in your code or in a reference assembly.