We use high-resolution ASKAP observations of galaxies in the Eridanus supergroup to study their HI, angular momentum and star formation properties, as part of the WALLABY pre-pilot survey efforts. The Eridanus supergroup is composed of three sub-groups in the process of merging to form a cluster. The main focus of this study is the Eridanus (or NGC 1395) sub-group. The baryonic specific angular momentum - baryonic mass ($j_{mathrm{b}} - M_{mathrm{b}}$) relation for the Eridanus galaxies is observed to be an unbroken power law of the form $j_{mathrm{b}} propto M_{mathrm{b}}^{0.57 pm 0.05}$, with a scatter of $sim 0.10 pm 0.01$ dex, consistent with previous works. We examine the relation between the atomic gas fraction, $f_{mathrm{atm}}$, and the integrated atomic disc stability parameter $q$ (the $f_{mathrm{atm}} - q$ relation), and find that the Eridanus galaxies deviate significantly from the relation owing to environmental processes such as tidal interactions and ram-pressure affecting their HI gas. We find that a majority of the Eridanus galaxies are HI deficient compared to normal star-forming galaxies in the field. We also find that the star formation among the Eridanus galaxies may be suppressed owing to their environment, thus hinting at significant levels of pre-processing within the Eridanus sub-group, even before the galaxies have entered a cluster-like environment.