The decay dynamics in molecular systems are important to consider for a wide number of phenomena and have implications across many fields of study. One common set of methods used to study these dynamics involve measurements of the time evolution of the excited state enhancement/suppression of nonlinear spectroscopic signals. Here we develop the novel technique of ultrafast transient polarization spectroscopy which allows us to measure decay dynamics in molecular systems using a polarization sensitive technique based on the optical Kerr effect. This is a three pulse technique where an exciting-pump pulse brings a portion of a sample into an electronic excited state and a pair of probing pulses measure changes in the sample's intensity dependent refractive index as a function of time delay. We then apply this technique to the study of neat liquid nitrobenzene where we measure oscillations in the dephasing time that we associate with oscillatory wave packet motion on the $S_1$ excited state. We then develop a set of theoretical methods that can be applied to study these polarization sensitive signals starting from a foundation in quantum chemistry. We also introduce a formalism for the projected density matrix which allows for an implicit transformation of lab frame signals into a molecular frame representation given a polarization sensitive measurement. These methods are then used to simulate the electronic response from a number of polarization sensitive signals with applications discussed.