This experiment is said in the literature probably to have disproved more theories than any other experiment in the history of physics (url).
The structural asymmetry we are sensitive to is so small that, if the neutron were expanded to the size of the Earth, the distortion would be less than a tenth of the thickness of a human hair.
If the structural asymmetry we're sensitive to were expanded to the size of, e.g., a football, then a football expanded by the same factor would be the size of the visible Universe.
The neutron "clock" runs at 30 Hz, or 1800 rpm; about the same as a car engine. We can measure the frequency so precisely that we'd be sensitive to an extra one turn per year on top of it.
We can sense energy changes of 10-21 eV, or 10-42 J; that's something like a million million million million million million million millionth of the amount of energy you need to boil water for a cup of tea.
The developments in precision frequency measurements needed for the first nEDM experiment, back in 1950, led ultimately to atomic clocks, NMR and MRI, GPS...