Strong UV-written Bragg gratings written in 50 µm-diameter cladding single mode fibers compatible with conventional fiber couple core guided light to dozens of cladding modes distributed across 140 nm in the 1400-1600 nm region, without the need for complex symmetry breaking mechanisms such as tilted, laterally offset, or localized gratings. The extent of the coupling to high order modes and the smaller cladding diameter both contribute to increasing the sensitivity to surrounding refractive index changes by more than one order of magnitude, and to an increased spacing between mode resonances to facilitate unambiguous measurements of larger index changes between 1.3 and 1.44. These improvements are confirmed by theoretical and experimental studies that also cover the temperature and strain differential sensitivities of the cladding mode resonances for complete multiparameter sensing capability.