The radial profiles of gas, stars, and far-ultraviolet radiation in 20 dwarf Irregular galaxies are converted to stability parameters and scale heights for a test of the importance of two-dimensional (2D) instabilities in promoting star formation. A detailed model of this instability involving gaseous and stellar fluids with self-consistent thicknesses and energy dissipation on a perturbation crossing time gives the unstable growth rates. We find that all locations are effectively stable to 2D perturbations, mostly because the disks are thick. We then consider the average volume densities in the midplanes, evaluated from the observed H i surface densities and calculated scale heights. The radial profiles of the star-formation rates are equal to about 1% of the H i surface densities divided by the free fall times at the average midplane densities. This 1% resembles the efficiency per unit free fall time commonly found in other cases. There is a further variation of this efficiency with radius in all of our galaxies, following the exponential disk with a scale length equal to about twice the stellar mass scale length. This additional variation is modeled by the molecular fraction in a diffuse medium using radiative transfer solutions for galaxies with the observed dimensions and properties of our sample. We conclude that star formation is activated by a combination of three-dimensional gaseous gravitational processes and molecule formation. Implications for outer disk structure and formation are discussed.