General equations are derived for differential cross sections for collisions between anisotropic molecular ensembles and electrons or atoms. In the obtained expressions geometrical and dynamical factors are separated. The initial anisotropic axis distribution is characterized by ''order parameters''; the information on the dynamics is contained in ''steric factors''. The results can be used to analyze experimental results and also as a basis for numerical calculations. Several examples are discussed in order to point out the geometrical importance of the relevant parameters for diatomic and polyatomic molecules. As an illustration, all relevant steric factors are numerically calculated for elastic collisions between electrons and anisotropic ensembles of CO molecules.