Yes you can go wild nesting ternaries. I find this version to be fairly readable:

var foo = (
  bar === 'a' ? 1 : // if 
  bar === 'b' ? 2 : // else if 
  bar === 'c' ? 3 : // else if
  null // else 
);

but that's not a widely shared opinion, and you should probably stick to if/else or switch when working on a team.

The syntax would be:

var icon = (area == 1) ? icon1 : (area == 2) ? icon2 : icon0;

But this is starting to get complicated. You may well be better off just creating a function to do this work instead:

var icon = getIcon(area);

function getIcon(area) {
  if (area == 1) { 
    return icon1; 
  } else if (area == 2) { 
    return icon2; 
  }

  return icon0;
}