We have performed a series of 56 sufficiently long molecular dynamics simulations of aqueous alkali halide solutions at infinite dilution and also at a higher concentration at 298 and 258 K and at 7 different pressures ranging from 0.1 to 875 MPa to investigate the role of ion screening in the pressure dependence of various dynamical and hydrogen bond properties of aqueous ionic solutions. We found that the orientational relaxation at both temperatures and the ion conductance and diffusion at the supercooled temperature show anomalous behavior with the application of pressure. The extent of the anomaly decreases somewhat in the concentrated solution because of ion screening effects. Correlations of these pressure-induced dynamical changes with the changes of hydrogen bond properties of the aqueous solutions are discussed.