First, let me say there is no definitive proof that solar (or geomagnetic) activity increase
the likelihood of strong earthquakes.
That said, there has been a lot of circumstantial evidence that there is a relation.
For example over the past 60 years, seismic activity has tended to increase on an
approximately 11-year cycle. Some claim a half cycle of 5.6 years as well. This
period is the same as the interval between maxima in solar activity.
There is also statistical evidence that in some areas (such as areas where fluids
are involved in seismic events - like mid-ocean ridges, volcanic centers and hydrothermal
centers such as the Geysers and Yellowstone) strong increases in seismicity
often follow strong solar or geomagnetic storms.
These correlations may be merely statistical flukes, however, they may also
require some explaining. So, physicists, being who they are have come up with
several theoretical scenarios:

1) When a solar storm hits the earth, the earth acts like a windchime and starts
vibrating in the solar wind. This vibration (called free-earth oscillations) can trigger
small earthquakes which in turn could trigger larger earthquakes.

2) The solar storm and associated magnetic and electrical currents and fluctuations
associated with the storm cause eddy currents in the earth's core. These eddies
drain some of the rotational motion of the earth causing a rapid acceleration or
deceleration (this is observed) in the earth's rotation. Tectonic plates have mass
and inertia. If the interior start spinning at a slower rate than the exterior, then
the plates on the exterior of the earth will tend to continue moving as they were
due to the laws of motion. This causes a differential motion between the plates
and the mantle beyond that caused by convection, and earthquakes are the
result of this motion.

3) When a geomagnetic storm is caused by either solar activity or by cosmic
radiation storms, electrical currents form in belts around the earth. These currents
tend to be concentrated over the auroral (about 2000 km from the N and S
magnetic poles) regions (called auroral electrojets), and over the geomagnetic
equator (called equatorial electrojets). Moving currents of electrons induce
similar currents in other conductors such as ore bodies in the earth. These
earth currents (called telluric currents) begin moving about and get stopped
at vertical faults where the geology is different on one side of the fault from the
other. The fault then acts as a kind of giant capacitor, storing up electrical energy
until something like an earthquake occurs.

4) The induced electrical currents transform their energy to heating (called
Ohmic heating). This heating, while miniscule can expand magma chamber
enough to cause volcanism (much like squeezing a tube of toothpaste) or at
least pressure on the upper hard crusts to these chambers. These also
result in earthquakes.

5) In small cracks the tips of the cracks are close enough that an electric
charge would tend to cause the two sides of the crack to repel each other.
This can lead to motion at crack tips due to electrical repulsion. Since this
is where all earthquake begin (at crack tips), this might be the most direct
possibility.

Your question regarding your position with relation to the onset of an
geomagnetic storm is also pertinent. When the earth is hit by the shockwave
from a solar storm, the ionosphere and upper atmospheric layers are pushed
ahead of the shock wave on the side facing the sun, and expanded into a
tail on the side opposite the sun (sub-solar and anti-solar respectively). The
regions between are generally about the same as when no storm is occurring.
The main effects, then are in the area directly under the sun (the direction
the shock wave is coming from) and those directly opposite. This agitation
of upper atmospheric layers by solar storms leads to a final hypothesis:

6) Solar storms cause weather phenomena which start in the upper atmosphere
(perhaps like large tornado cells). These storms interact with the earth and
cause sudden changes in the rotational velocity - see hypothesis 2 above for
the results of this.

Anyway, that is a brief review. Anyone is welcome to add or subtract from
it, I may have some of the details in error.