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.