Use OnMouseOver with an object that has a collider (this uses raycasting, but you don't have to program it explicitly):

function OnMouseOver () {
   if (Input.GetMouseButtonDown(1)) {
      // Do right-click stuff here
   }
}

There's OnMouseDown too, where you don't have to check the input, but that's only for left-clicking.

erric's answer is correct. just as an additional note i should say. inside the if statement you should set a variable to true and then in GUI do something like this.

function OnGUI ()
{
   if (clicked == true)
{
   //show buttons in a vertical group here
}
}

in mouse leave or other events you should set this variable to false for the GUI to hide it.