The major abdominal muscles involved in expiration are the internal obliques and external obliques and the transverse abdominis. The rectus abdominis becomes involved when there is maximum expiration and you flex the spine to squeeze out more air.
When at rest, the abdominals are not involved. Expiration occurs naturally due mainly to the elastic recoil of the thoracic cage. In forced expiration however, many changes take place. The internal and external obliques and the transverse abdominis participate vigorously. They are also involved in coughing, singing, birthing, straining (as in weightlifting) and defecation.
Because of the difficulty in isolating the transverse abdominis with EMGs, their function is based on their anatomy and structure. They are ideally suited for expiration and holding in the abdominal viscera. You may read about trainers saying you should contract the transverse abdominis in a particular exercise, but it appears to be impossible to isolate this one muscle from the other abdominal muscles.
The external and internal obliques are ideally suited for expiration because of their cross movements. They are very effective in compressing the abdominal wall. When coupled with the transverse abdominis they are very powerful in expelling the air quickly. The rectus abdominis on the other hand, is not involved, unless the spine also undergoes flexion.