I am not a 100% sure on what you are trying to achive but anyways:

function Update ()
{
var horizontalSpeed = Input.GetAxis("Horizontal");

var verticalSpeed = Input.GetAxis("Vertical");

transform.position += transform.forward * verticalSpeed * Time.deltaTime;

transform.positon += transform.right * horizontalSpeed * Time.deltaTime;
}

You only need to use 1 axis at the time. Since Input.GetAxis returns form -1 to 1 and therefor it is unneccersary to use this twice:

if (Input.GetAxis("Vertical"))
{      
transform.position += transform.forward * moveSpeed * Time.deltaTime;
}   
if (Input.GetAxis("Vertical"))
{      
transform.position += -transform.forward * moveSpeed * Time.deltaTime;
}

but simply use:

   var verticalSpeed = Input.GetAxis("Vertical");

   transform.position += transform.forward * verticalSpeed * Time.deltaTime;

You don't actually need two seperate ones. Just use one for each! Horizontal means both left and right, with one (I think left, but check this) being negative and the other positive. Same with Vertical --- it accounts for both. So just lose some of the excess statements, and it'll be fine.