It's a question that simply cannot be answered by classical physics.
It was a big problem in the 19th Century that contemporary theory suggested that the most energetically favourable configuration of charged particle would be 'all on top of each other'.
It was only when Heisenberg came along that the 'exclusion principle' was formulated.
The idea is that these new laws predicted that two particles (like the neutral ones you mention) can never end up in the same place. As they get too close, the quantum mechanical 'degenerecy pressure' prevents them from ever 'overlapping'.
Not a great explanation, apologies.
Van der Waals forces are just one particular manifestation of classical electrostatics.
Incidentally, this degenerecy pressure is also the reason we never 'touch' anything ourselves. Classical electrostatics cannot account for that. Why would the atoms in our hand repel the atoms in the brick (or whatever)? Clasically, they would attract (due to polarisation within the atom), and then overlap, with the protons all hugging up to the electrons in a big particle soup.
Amazing to think that no-one before the beginning of the 20th century could even begin to explain why we don't fall through the floor.