Studies of prompt triple and four-fold, γ-γ-γ and γ-γ-γ-γ, coincidence data observed with Gammasphere following the spontaneous fission of 252 Cf have significantly expanded our knowledge and identified new features of the variety of structures in fourteen neutron-rich nuclei and traced their changes over long isotopic chains in Ru, Pd and Cd nuclei. Evolution with changing neutron number and onset of wobbling motions were observed in Ru and Pd isotopes. Evolution from chiral symmetry breaking to disturbed chirality was identified from 110,112 Ru to 112,114,116 Pd and from 110,112 Ru to 108 Ru. Quasi-particle couplings, quasi-rotations and triaxiality were suggested in Cd isotopes. A complete but complex picture of shape evolution and coexistence was revealed in Pd isotopes. Based on the systematic studies in the mass region, maximal triaxiality is reached in 112 Ru and 114 Pd, for N=68, four neutrons more than predicted in theoretical calculations. The Cd isotopes were observed to have small quadrupole deformation.