The structures and relaxation dynamics of I-2(-) embedded in clusters of N2O molecules are studied by Monte Carlo and molecular dynamics simulations. The equilibrium structures of I-2(-) (N2O)(n) clusters are obtained as a function of cluster size and the closing of the first solvation shell is found to occur at n=13, consistent with experimental observation. By comparing with the previous studies with different types of solvent molecules, it is found that differences in solvent polarity lead to noticeable changes in equilibrium structures and caging dynamics of clusters. N2O clusters tend to form more symmetric, spread-out solvent configurations, resulting in a weaker solvent electric field being exerted on the solute. The localization of the charge distribution for large internuclear separations happens for longer bond length and much more rapidly in I-2(-) (N2O)(16) than in I-2(-) (CO2)(16) clusters. Molecular dynamics simulations showed that I-2(-) vibrational relaxation is very rapid, losing almost 90% of its internal energy within 1 ps of recombination. It is suggested that the change of I-2(-) charge distribution provides an efficient mechanism for energy transfer from the anion to the surrounding solvents. The N2O solvent with permanent dipole moment exhibits a slightly shorter relaxation time than the nonpolar CO2 solvent. The electrostatic interactions are found to be major driving forces for the compression of the solute throughout the relaxation processes. The effects of solvent flexibility on the relaxation dynamics are investigated for I-2(-) embedded in clusters of flexible N2O solvents. It is found that including the flexibility of the N2O molecules has minimal effect on the vibrational relaxation dynamics of I-2(-) (N2O)(16) clusters.