The `else if` is the problem. With the `else if`, it **wont** run the rest of the code in the else if any one in the top is true. What you do is **remove** the else ifs and simply use multiple if statements.

     private void MovePlayer()
        {
            if (Input.GetKey(KeyCode.W)) // Up
            {
                if (Input.GetKey(KeyCode.A)) //Up and left
                {
                    rigidB.velocity += new Vector3(-moveSpeed, 0, moveSpeed);
                }
                else if (Input.GetKey(KeyCode.D)) //Up and right
                {
                    rigidB.velocity += new Vector3(moveSpeed, 0, moveSpeed);
                }
                else
                {
                    rigidB.velocity += new Vector3(0, 0, moveSpeed);
                }
            }
            if (Input.GetKey(KeyCode.S)) // Down
            {
                rigidB.velocity += new Vector3(0, 0, -moveSpeed);
            }
            if (Input.GetKey(KeyCode.A)) // Left
            {
                rigidB.velocity += new Vector3(-moveSpeed, 0, 0);
            }
            if (Input.GetKey(KeyCode.D)) // Right
            {
                rigidB.velocity += new Vector3(moveSpeed, 0, 0);
            }
        }