First and foremost you need an extra check, make sure that the sound is not 'already' playing before you play it:

if (... && !audio.isPlaying) audio.Play();

But that won't totally fix it, so let's check out what you said and try to go from there:

1- "while holding down the "w" key I start holding down the "d" key: *audio restarts from beginning" - That's right, that's what you told it to here:

 if((Input.GetKeyDown("w") || Input.GetKeyDown("a") || Input.GetKeyDown("s") ||   
     Input.GetKeyDown("d")) && isGrounded) {
     audio.Play();
 }

Which basically translates to: "any time I press 'w', 'a', 's' or 'd' and I'm grounded" -> play the sound from the beginning.

2- "I the let go of the "d" while still holding the "w" key: audio stops" That's right again, that's what you told it to do here:

 if((Input.GetKeyUp("w") || Input.GetKeyUp("a") || Input.GetKeyUp("s") ||
    Input.GetKeyUp("d")) && isGrounded) {
    audio.Stop();
 }

Which basically says: "If I let go off of 'w', or 'a', or 's', or 'd' and I'm grounded" -> stop the sound.

So let's get your comparison operators right, and knock out your confusion about Input.GetKey/Input.GetButton family.

1. Input.GetButtonDown/Input.GetKeyDown returns true on the first frame you press button on, and then as frames progress, holding down the button, Input.GetButtonDown/Input.GetKeyDown will return false.

2. To say "if I'm holding X button" use Input.GetButton/Input.GetKey instead, which will return true while the button is being pressed.

3. Input.GetButtonUp/Input.GetKeyUp returns true the moment you let go of the key (key goes up)

More info on Input.GetKey and Input.GetButton families can be found here.

Armed with the information in your possession now, you should be able to fix the problem and know what went wrong with your approach :)

In case you're lazy here's how it could look like:

 function Update()
 {
     var isMoving = Input.GetKey("w") || Input.GetKey("a") || Input.GetKey("s") || Input.GetKey("d");

     // which translates to: "If I'm holding 'w', 'a', 's' or 'd' -> I'm moving"

     if(isMoving && controller.isGrounded)
     {
        if (!audio.isPlaying)
        {
           audio.Play();
        }
     }
     else audio.Stop();
 }