  This paper is a continuation of arXiv:1201.1102. We investigate the orbit
closures for the class of representations of simple algebraic groups associated
to various gradings on the simple Lie algebra of type $E_7$. The methods for
classifying the orbits for these actions were developed by Vinberg . We give
the orbit descriptions, the degeneration partial orders, and indicate normality
of the orbit closures. We also investigate the rational singularities,
Cohen-Macaulay and Gorenstein properties for the orbit closures. We give the
information on the defining ideals of orbit closures.
