A new method has been developed to predict acoustic scattering by weakly scattering objects with three-dimensional variability in sound speed and density. This variability can take the form of inhomogeneities within the body of the scatterer and/or geometries where the acoustic wave passes through part of the scattering body, into the surrounding medium, and back into the body. This method applies the distorted wave Born approximation (DWBA) using a numerical approach that rigorously accounts for the phase changes within a scattering volume. Ranges of validity with respect to material properties and numerical considerations are first explored through comparisons with modal-series-based predictions of scattering by fluid-filled spherical and cylindrical fluid shells. The method is then applied to squid and incorporates high resolution spiral computerized tomography (SCT) scans of the complex morphology of the organism. Target strength predictions based on the SCT scans are compared with published backscattering data from live, freely swimming and tethered squid. The new method shows significant improvement for both single-orientation and orientation-averaged scattering predictions over the DWBA-homogeneous-prolate-spheroid model.