  This is the continuation of an earlier work where Godel-type metrics were
defined and used for producing new solutions in various dimensions. Here a
simplifying technical assumption is relaxed which, among other things,
basically amounts to introducing a dilaton field to the models considered. It
is explicitly shown that the conformally transformed Godel-type metrics can be
used in solving a rather general class of Einstein-Maxwell-dilaton-3-form field
theories in D >= 6 dimensions. All field equations can be reduced to a simple
"Maxwell equation" in the relevant (D-1)-dimensional Riemannian background due
to a neat construction that relates the matter fields. These tools are then
used in obtaining exact solutions to the bosonic parts of various supergravity
theories. It is shown that there is a wide range of suitable backgrounds that
can be used in producing solutions. For the specific case of (D-1)-dimensional
trivially flat Riemannian backgrounds, the D-dimensional generalizations of the
well known Majumdar-Papapetrou metrics of general relativity arise naturally.
