This is Lords of the Psychon by Daniel F. Galouye.
Please note that it was "Horror day", not "Hell day" but pretty much everything else matches.
The novel is set 15 years after the devastation of earth. A band of
holdout soldiers remain steadfast to their military/defensive duty,
and are based in a deserted junior college in the shadow of a strange,
towering, alien City of Force. Wherever the aliens have established
themselves, they have raised up great walled cities comprising huge
buildings shaped like cylinders, pyramids, cubes, rhombohedrons,
semi-transparent prisms, and balls. Electric equipment all over the
earth has been shut down by the aliens, and all of human civilization
has been driven back to a coal and steam-based technology. The Cities
of Force are the home of the “Spheres”. They are large floating aliens
that generally ignore humans except when they decide to “select”
someone. Then they hover and float through the air, crackling with
static electricity and hunting the selected person apparently for
sport. Spheres can travel right through walls and hillsides in their
pursuit of the selected people. When they finally run down the prey,
they throw lightning bolts to kill the human. The Spheres also get
active around the time of Horror Day, an annual event when a grid of
energy forms over the earth and somehow inflicts incredible physical
and mental torture on the earthlings, which takes months for the
populace to recover from.
https://en.wikipedia.org/wiki/Lords_of_the_Psychon