Using Gammasphere data on prompt gamma rays from spontaneous fission of 252Cf, we propose energy-level schemes for 110,111,112, & 113Rh (Z=45). The fission-gamma data complement earlier studies of others on beta decay of fission products in that prompt fission gammas mainly populate yrast or near-yrast levels, while beta decay populates lower-spin levels. For the odd-A rhodium nuclei studied here, their ground bands and collective sidebands are compared with model calculations using triaxial-shaped nucleus with one odd quasi-proton. The energies and E2 transition rates are best fit by a shape slightly to the prolate side of maximum triaxiality, namely, gamma = 28 deg. The model calculations also show a K=1/2+ band with energies not in good agreement with a corresponding exerimental band. The experimental 1/2+ band is regarded as an intruder band from a prolate-driving proton orbital 1/2 above the Z=50 closed shell. This intruder band, seen in other odd-A Rh isotopes, is probably more deformed and prolate and would not be expected to be fit at the same triaxial shape parameter as the 7/2+ ground band. We observe a band-crossing (backbending) in the odd-A ground bands above spins of about 21/2. The odd-odd nuclei 110 and 112 Rh show mainly a single band with no backbending up to higherfrequency than the backbend in the odd-A isotopes. It is concluded that the backbend is due to alignment of a pair of h11/2 neutrons.