This paper is the third in a series on tests of gravity using observations of stars and nearby dwarf galaxies. We carry out four distinct tests using published data on the kinematics and morphology of dwarf galaxies, motivated by the theoretical work of Hui et al. (2009) and Jain and Vanderplas (2011). In a wide class of gravity theories a scalar field couples to matter and provides an attractive fifth force. Due to their different self-gravity, stars and gas may respond differently to the scalar force leading to several observable deviations from standard gravity. HI gas, red giant stars and main sequence stars can be displaced relative to each other, and the stellar disk can display warps or asymmetric rotation curves aligned with external potential gradients. To distinguish the effects of modified gravity from standard astrophysical phenomena, we use a control sample of galaxies that are expected to be screened from the fifth force. In all cases we find no significant deviation from the null hypothesis of general relativity. The limits obtained from dwarf galaxies are not yet competitive with the limits from cepheids obtained in our first paper, but can be improved to probe regions of parameter space that are inaccessible using other tests. We discuss how our methodology can be applied to new radio and optical observations of nearby galaxies.

24 pages, 12 figures