We study the evolution of nuclear wave packets launched in molecular nitrogen, oxygen, and carbon monoxide by intense 8-fs infrared pulses. We use velocity map imaging to measure the momentum of the ion fragments when these wave packets are interrogated by a second such pulse after a variable time delay. Both quasibound and dissociative wave packets are observed. For the former, measurements of bound-state oscillations are used to identify the participating states and, in some cases, extract properties of the relevant potential-energy surfaces. Vibrational structure is resolved in both energy and oscillation frequencies for the cations of oxygen and carbon monoxide, displaying the same quantum wave-packet motion in both energy and time domains. In addition, vibrational structure is seen in the dication of carbon monoxide in a situation where the energy resolution by itself is inadequate to resolve the structure.