Wait a few seconds for the code to run, and then look at the output in the Console Window (bottom pane on that page).
Here's the output of the Deserialization.

You have to deserialize the JSON into an Array of Vars. Like So.
Dim varses() = Newtonsoft.Json.JsonConvert.DeserializeObject(Of Vars())(rawresp)
Notice also that the literal JSON string has the name and value strings enclosed in double quotes.
You were probably getting invalid JSON format error due to the missing extra quote around each name and each value.
rawresp = "[{""Var1"":""data1"",""Var2"":""data2"",""Var3"":""data3"",""Var4"":""data4""}]"
Also be sure to check for empty array etc before attempting to access the items inside.
Here's the entire code listing that works.
Imports System
Imports Newtonsoft.Json
Imports Newtonsoft.Json.Linq
' Author: Shiva Manjunath
' Author's Stackoverflow Profile: http://stackoverflow.com/users/325521/shiva
Public Module Module1
Public Sub Main()
Dim rawresp As String
rawresp = "[{""Var1"":""data1"",""Var2"":""data2"",""Var3"":""data3"",""Var4"":""data4""}]"
Console.WriteLine("Raw JSON : " + rawresp)
Console.WriteLine()
Console.WriteLine("---BEGIN JSON Deserialization")
Dim varses() = Newtonsoft.Json.JsonConvert.DeserializeObject(Of Vars())(rawresp)
' Loop over each Var in the Array of Vars.
For Each oneVar As Vars In varses
' Avoid Nothing vars.
If oneVar IsNot Nothing Then
Console.WriteLine(" Var1 = " + oneVar.Var1)
Console.WriteLine(" Var2 = " + oneVar.Var2)
Console.WriteLine(" Var3 = " + oneVar.Var3)
Console.WriteLine(" Var4 = " + oneVar.Var4)
End If
Next
Console.WriteLine("---END JSON Deserialization")
End Sub
End Module
Public Class Vars
Public Property Var1 As String
Public Property Var2 As String
Public Property Var3 As String
Public Property Var4 As String
End Class