We report measurements of the observed cross sections for $e^+e^-toomega pi^+pi^-$, $omega K^+K^-$, $omega pbar p$, $K^+K^-rho^0pi^0$, $K^+K^-rho^+pi^-+c.c.$, $K^{*0}K^-pi^+pi^0+c.c.$, $K^{*+}K^-pi^+pi^-+c.c.$, $phipi^+pi^-pi^0$ and $Lambda bar Lambda pi^0$ at $sqrt s=$ 3.773 and 3.650 GeV. Upper limits (90% C.L.) are given for observed cross sections and for $psi(3770)$ decay branching fractions for production of these final states. These measurements are made by analyzing the data sets of 17.3 pb$^{-1}$ collected at $sqrt{s}=3.773$ GeV and 6.5 pb$^{-1}$ collected at $sqrt{s}=3.650$ GeV with the BES-II detector at the BEPC collider.