  Several Einstein-Sasaki 7-metrics appearing in the physical literature are
fibered over four dimensional Kahler-Einstein metrics. Instead we consider here
the natural Kahler-Einstein metrics defined over the twistor space Z of any
quaternion Kahler 4-space, together with the corresponding Einstein-Sasaki
metrics. We work out an explicit expression for these metrics and we prove that
they are indeed tri-Sasaki. Moreover, we present an squashed version of them
which is of weak $G_2$ holonomy. We focus in examples with three commuting
Killing vectors and we extend them to supergravity backgrounds with $T^3$
isometry, some of them with $AdS_4\times X_7$ near horizon limit and some
others without this property. We would like to emphasize that there is an
underlying linear structure describing these spaces. We also consider the
effect of the $SL(2,R)$ solution generating technique presented by Maldacena
and Lunin to these backgrounds and we find some rotating membrane
configurations reproducing the E-S logarithmic behaviour.
