Using 281pb-1 of data collected with the CLEO-c detector, we report on first observations and measurements of Cabibbo-suppressed decays of D mesons in the following six decay modes: π+π-π0π0, π+π+π-π-π0, π+π0π0, π+π+π-π0, ηπ0, and ωπ+π-. Improved branching fraction measurements in eight other multipion decay modes are also presented. The measured D→ππ rates allow us to extract the ratio of isospin amplitudes A(ΔI=3/2)/A(ΔI=1/2)=0.420±0. 014(stat)±0.016(syst) and the strong phase shift of δI=(86. 4±2.8±3.3)°, which is quite large and now more precisely determined.