  We present the highest resolution and sensitivity $\sim1.4\,$GHz continuum
observations of the Eridanus supergroup obtained as a part of the Widefield
ASKAP L-band Legacy All-sky Blind surveY (WALLABY) pre-pilot observations using
the Australian Square Kilometer Array Pathfinder (ASKAP). We detect 9461
sources at 1.37 GHz down to a flux density limit of $\sim0.1$ mJy at
$6.1''\times 7.9''$ resolution with a mean root-mean-square (RMS) of 0.05
mJy/beam. We find that the flux scale is accurate to within 5% (compared to
NVSS at 1.4 GHz). We then determine the global properties of eight Eridanus
supergroup members, which are detected in both radio continuum and neutral
hydrogen (HI) emission, and find that the radio-derived star formation rates
(SFRs) agree well with previous literature. Using our global and resolved radio
continuum properties of the nearby Eridanus galaxies, we measure and extend the
infrared-radio correlation (IRRC) to lower stellar masses and inferred star
formation rates than before. We find the resolved IRRC to be useful for: 1)
discriminating between AGN and star-forming galaxies (SFGs); 2) identifying
background radio sources; and 3) tracing the effects of group environment
pre-processing in NGC 1385. We find evidence for tidal interactions and
ram-pressure stripping in the HI, resolved spectral index and IRRC morphologies
of NGC 1385. There appears to be a spatial coincidence (in projection) of
double-lobed radio jets with the central HI hole of NGC 1367. The destruction
of polycyclic aromatic hydrocarbons (PAHs) by merger-induced shocks may be
driving the observed WISE W3 deficit observed in NGC 1359. Our results suggest
that resolved radio continuum and IRRC studies are excellent tracers of the
physical processes that drive galaxy evolution and will be possible on larger
sample of sources with upcoming ASKAP radio continuum surveys.
