Strongly Typed Access to Embedded Resources

You're almost there. I have a couple of functions I use for this. You can do somehting very similar for images. I'm not sure it's worth creating properties like you want (you can do that through the Resources tab of the project properties if you insist).

/// <summary>
    /// Gets an open stream on the specified embedded resource. It is the
    /// caller's responsibility to call Dispose() on the stream.
    /// The filename is of the format "folder.folder.filename.ext"
    /// and is case sensitive.
    /// </summary>
    /// <param name="assembly">The assembly from which to retrieve the Stream.</param>
    /// <param name="filename">Filename whose contents you want.</param>
    /// <returns>Stream object.</returns>
    public static Stream GetStream(Assembly assembly, string filename)
    {
        string name = String.Concat(assembly.GetName().Name, ".", filename);
        Stream s = assembly.GetManifestResourceStream(name);
        return s;
    }

    /// <summary>
    /// Get the contents of an embedded file as a string.
    /// The filename is of the format "folder.folder.filename.ext"
    /// and is case sensitive.
    /// </summary>
    /// <param name="assembly">The assembly from which to retrieve the file.</param>
    /// <param name="filename">Filename whose contents you want.</param>
    /// <returns>String object.</returns>
    public static string GetFileAsString(Assembly assembly, string filename)
    {
        using (Stream s = GetStream(assembly, filename))
        using (StreamReader sr = new StreamReader(s))
        {
            string fileContents = sr.ReadToEnd();
            return fileContents;
        }
    }

On a resource file you won't be able to have intellisense to build your sql script compare to have them as separate files in your project. You can create a helper class to access them in a strong type fashion:

public class Scripts
{
    public static string Sql1
    {
        get
        {
            return GetResource("sql1.sql");
        }
    }

   public static string Sql2
   {
        get
        {
           return GetResource("sql2.sql");
        }
   }

    private static string GetResource(string name)
    {
        var assembly = Assembly.GetExecutingAssembly();
        using(var stream = new StreamReader(assembly.GetManifestResourceStream("Myproject.Sql." + name)))
        {
            return stream.ReadToEnd();
        }
    }
}

For example, in Dapper, you can access your scripts like this:

using(var db = new SqlConnection("yourconnectionstring")){
    db.Open();
    var results = db.Query(Scripts.Sql1);
}