  We construct new families of solutions of the heterotic G$_2$ system on
squashed homogeneous 3-Sasakian manifolds, that is, using squashed metrics on
either the 7-sphere or the Aloff-Wallach space $N_{1,1}$. We obtain AdS$_3$
solutions for all values of the squashing parameter $s$ except for the
nearly-parallel G$_2$ value $s=1/\sqrt{5}$, for which we don't find any
solutions. Along the process, we construct different G$_2$-instanton
connections on bundles over these squashed manifolds.
