We probe the time-dependent ionization dynamics of impulsively excited rotational wave packets of ${\mathrm{N}}_{2}, {\mathrm{CO}}_{2}$, and ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$ using broadband ultraviolet pulses centered at 262 nm. Photoelectron momentum distributions recorded by velocity-map imaging show a strong dependence on alignment, on multiphoton order, and on the electronic and vibrational states of the cation. We show that substantial information about the molecular-frame photoelectron angular distribution can be obtained from the high-order laboratory-frame asymmetry parameters without any prior knowledge of the photoionization process. We also compare few-photon ionization with one-photon ionization and strong-field ionization.