Clouds play a crucial role in Earth's radiative budget, yet their climate feedbacks are poorly understood. The advent of space-borne high resolution spectrometers probing the O<sub>2</sub> A band, like GOSAT and OCO-2, could make it possible to simultaneously retrieve vertically resolved cloud parameters that play a vital role in Earth's radiative budget, thereby allowing a reduction of the corresponding uncertainty due to clouds. Such retrievals would also facilitate air mass bias reduction in corresponding measurements of CO<sub>2</sub> columns. <br><br> In this work, the hyperspectral, polarimetric response of the O<sub>2</sub> A band to mainly three important cloud parameters, viz., optical thickness, top height and droplet size has been studied, revealing a different sensitivity to each for the varying atmospheric absorption strength within the A band. Cloud optical thickness finds greatest sensitivity in intensity measurements, the sensitivity of other Stokes parameters being limited to low cloud optical thicknesses. Cloud height had a negligible effect on intensity measurements at non-absorbing wavelengths but finds maximum sensitivity at an intermediate absorption strength, which increases with cloud height. The same is found to hold for cloud geometric thickness. The geometry-dependent sensitivity to droplet size is maximum at non-absorbing wavelengths and diminishes with increasing absorption strength. It has been shown that significantly more information on droplet size can be drawn from multi-angle measurements. We find that, in the absence of sunglint, the backscatter hemisphere (scattering angle larger than 90°) is richer in information on droplet size, especially in the glory and rainbow regions. It has been shown that <i>I</i> and <i>Q</i> generally have differing sensitivities to all cloud parameters. Thus, accurate measurements of two orthogonal components <i>I</i><sub>P</sub> and<i>I</i><sub>S</sub> (as in GOSAT) are expected to contain more information than measurements of only <i>I</i>, <i>I</i><sub>h</sub> or <i>I</i><sub>v</sub> (as in the case of OCO-2).