The cross section of the process $e^+e^-topi^+pi^-pi^0$ is measured with a precision of 1.6% to 25% in the energy range between $0.7$ and 3.0 GeV using the Initial State Radiation method. A data set with an integrated luminosity of $2.93$fb$^{-1}$ taken at the center-of-mass energy of $sqrt{s}=3.773$GeV with the BESIII detector at the BEPCII collider is used. The product branching fractions for $omega$, $phi$, $omega(1420)$, and $omega(1650)$ are measured to be $mathcal{B}(omegato e^+e^-) times mathcal{B}(omega to pi^+pi^-pi^0)=(6.94pm0.08pm0.16) times 10^{-5}$, $mathcal{B}(phito e^+e^-) times mathcal{B}(phitopi^+pi^-pi^0) = (4.20pm0.08pm0.19) times 10^{-5}$, $mathcal{B}(omega(1420)to e^+e^-) times mathcal{B}(omega(1420) to pi^+pi^-pi^0) = (0.84pm0.09pm0.09) times 10^{-6}$, and $mathcal{B}(omega(1650) to e^+e^) times mathcal{B}(omega(1650)to pi^+pi^-pi^0) = (1.14pm0.15pm0.15)times10^{-6}$, respectively. The branching fraction $mathcal{B}(J/psito pi^+pi^-pi^0)$ is measured to be $(2.188 pm 0.024 pm 0.024 pm0.040 (Gamma_{ee}^{J/psi}))%$, where $Gamma_{ee}^{J/psi}$ is the dileptonic width of $J/psi$. The first errors are of statistical, the second and third ones of systematic nature.
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