Aqueous solutions of 1-10, 1-20, and 2-20 electrolytes with an asymmetry in size of 2:15 are studied for several volume fractions between 4% and 44%. The use of an efficient Brownian dynamics simulation method allows the investigation of the structural and dynamical properties of these systems. The pair interaction potential between ions is modeled by a pairwise soft-core repulsion (1/r(9)) and the Coulomb interaction. Self-diffusion coefficients of both polyions and counterions are calculated. The residence times of counterions in the vicinity of polyions are also computed. It is shown that a crystallization of macroions in a face centered cubic phase occurs for the 1-20 and 2-20 electrolytes at the highest concentration. In the 1-10 electrolyte at the same volume fraction, the macroions stay in a disordered structure. In any case the residence time of counterions around polyions is relatively small. Indeed, the self-diffusion of counterions is slightly increased in the 2-20 electrolyte when the electrolyte concentration is increased, whereas it is roughly constant in the other systems. Finally, the self-diffusion coefficients of polyions decrease strongly with regards to the infinite dilution, especially as they are charged.