The Solar Wind ANisotropies (SWAN) all-sky hydrogen Lyman-alpha camera on the SOlar and Heliosphere Observer (SOHO) satellite makes daily images of the entire sky to monitor the three-dimensional distribution of solar wind and solar radiation via its imprint on the stream of interstellar hydrogen that flows through the solar system. In the process it also records the distribution of the hydrogen comae of comets. We report here the analyses of six comets originally from the Oort Cloud observed during the 2017–2020 period by SWAN: C/2015 V2 (Johnson), C/2019 Y1 (ATLAS), C/2017 T2 (PanSTARRS), C/2020 F8 (SWAN), C/2019 Y4 (ATLAS), and C/2019 U6 (Lemmon). Of these the nuclei of C/2019 Y4 (ATLAS) and C/2020 F8 (SWAN) both broke up on their inbound orbit before perihelion. The water production rates over the detectable portion of each comet's orbit are determined and discussed in light of the comet's dynamical sub-class of Oort Cloud comets.