The ab initio effective valence shell Hamiltonian (H-v) is used to compute the low lying vertical excitation energies and oscillator strengths for ethylene, trans-butadiene, benzene and cyclobutadiene. Calculated excitation energies and oscillator strengths of ethylene, trans-butadiene and benzene to various valence and Rydberg states are in good agreement with experiment and with values from other highly correlated computations. The present work further investigates the dependence of H-v computations on the nature and choice of the molecular orbitals and provides a comprehensive study of the convergence with respect to the enlargement of the valence space. Minimal valence space H-v computations yield very accurate estimates of the excitation energies for the low lying excited triplet states and are slightly poorer (a deviation of less than or equal to 0.5 eV from experiment) for low lying excited singlet states. More accurate low lying singlet state excitation energies are achieved by slightly enlarging the valence space to include Rydberg functions. The computed oscillator strengths from the H-v method are in excellent agreement with experiment and compare favorably with the best theoretical calculations. A very quick estimation of the transition dipoles and oscillator strengths may be obtained from second order H-v computations. The accuracy of these calculations is almost as good as those from the more expensive third order H-v computations and far superior to those from other quick methods such as the configuration interactions singles technique. Although no experimental data are available for the excitation energies and oscillator strengths of cyclobutadiene, our predicted values should be quite accurate and should aid in observing its pi --> pi* transitions. We also provide the first correlated computations of oscillator strengths for excited-->excited singlet and tripler transitions.