We explore the quantified morphology of atomic hydrogen (HI) disks in the Virgo cluster. These galaxies display a wealth of phenomena in their Hi morphology, e.g., tails, truncation and warps. These morphological disturbances are related to the ram-pressure stripping and tidal interaction that galaxies undergo in this dense cluster environment. To quantify the morphological transformation of the HI disks, we compute the morphological parameters of CAS, Gini, and M20 and our own GM for 51 galaxies in 48 HI column density maps from the VIVA project. Some morphological phenomena can be identified in this space of relatively low resolution HI data. Truncation of the HI disk can be cleanly identified via the Concentration parameter (C<1) and Concentration can also be used to identify HI deficient disks (1<C<5). Tidal interaction is typically identified using combinations of these morphological parameters, applied to (optical) images of galaxies. We find that some selection criteria (Gini-M20, Asymmetry, and a modified Concentration-M20) are still applicable for the coarse (~15 FWHM) VIVA HI data. The phenomena of tidal tails can be reasonably well identified using the Gini-M20 criterion (60% of galaxies with tails identified but with as many contaminants). Ram-pressure does move HI disks into and out of most of our interaction criteria: the ram-pressure sequence identified by Vollmer et al. (2009) tracks into and out of some of these criteria (Asymmetry based and the Gini-M20 selections, but not the Concentration-M20 or the GM based ones). Therefore, future searches for interaction using HI morphologies should take ram-pressure into account as a mechanism to disturb HI disks enough to make them appear as gravitationally interacting. One mechanism would be to remove all the HI deficient (C<5) disks from the sample, as these have undergone more than one HI removal mechanism.