The Virgo Filament Survey (VFS) is a comprehensive study of galaxies that reside in the extended filamentary structures surrounding the Virgo Cluster, out to 12 virial radii. The primary goal is to characterize all of the dominant baryonic components within galaxies and to understand whether and how they are affected by the filament environment. A key constituent of VFS is a narrowband Hα imaging survey of over 600 galaxies, VFS-Hα. The Hα images reveal detailed, resolved maps of the ionized gas and massive star formation. This imaging is particularly powerful as a probe of environmentally induced quenching because different physical processes affect the spatial distribution of star formation in different ways. In this paper, we present the first results from the VFS-Hα for the NGC 5364 group, a low-mass ( log 10 ( M dyn / M ⊙ ) < 13 ) system located at the western edge of the Virgo III filament. We combine Hα imaging with resolved H i observations from MeerKAT for eight group members. These galaxies exhibit peculiar morphologies, including strong distortions in the stars and the gas, truncated H i and Hα disks, H i tails, extraplanar Hα emission, and off-center Hα emission. These signatures are suggestive of environmental processing such as tidal interactions, ram pressure stripping, and starvation. We quantify the role of ram pressure stripping expected in this group, and find that it can explain the cases of H i tails and truncated Hα for all but one of the disk-dominated galaxies. Our observations indicate that multiple physical mechanisms are disrupting the baryon cycle in these group galaxies.