The cross section of the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ was measured in the Spherical Neutral Detector experiment at the VEPP-2M collider in the energy region $\sqrt{s}=980--1380 \mathrm{MeV}.$ The measured cross section, together with the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ and $\ensuremath{\omega}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ cross sections obtained in other experiments, was analyzed in the framework of the generalized vector meson dominance model. It was found that the experimental data can be described by a sum of $\ensuremath{\omega},$ $\ensuremath{\varphi}$ mesons and two ${\ensuremath{\omega}}^{\ensuremath{'}}$ and ${\ensuremath{\omega}}^{\ensuremath{''}}$ resonances contributions, with masses ${m}_{{\ensuremath{\omega}}^{\ensuremath{'}}}\ensuremath{\sim}1490,$ ${m}_{{\ensuremath{\omega}}^{\ensuremath{''}}}\ensuremath{\sim}1790 \mathrm{MeV}$ and widths ${\ensuremath{\Gamma}}_{{\ensuremath{\omega}}^{\ensuremath{'}}}\ensuremath{\sim}1210,$ ${\ensuremath{\Gamma}}_{{\ensuremath{\omega}}^{\ensuremath{''}}}\ensuremath{\sim}560 \mathrm{MeV}.$ The analysis of the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ invariant mass spectra in the energy region $\sqrt{s}$ from 1100 to 1380 MeV has shown that for their description one should take into account the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ mechanism also. The phase between the amplitudes corresponding to the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\pi}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\pi}$ intermediate states was measured for the first time. The value of the phase is close to zero and depends on energy.