The detailed behavior of the in-plane infrared-active vibrational modes has been determined in AFe2As2 (A=Ca, Sr, and Ba) above and below the structural and magnetic transitions at TN=172, 195, and 138 K, respectively. Above TN, two infrared-active Eu modes are observed. In all three compounds, below TN, the low-frequency Eu mode is observed to split into upper and lower branches; with the exception of the Ba material, the oscillator strength across the transition is conserved. In the Ca and Sr materials, the high-frequency Eu mode splits into an upper and a lower branch; however, the oscillator strengths are quite different. Surprisingly, in both the Sr and Ba materials, below TN the upper branch appears to be either very weak or totally absent, while the lower branch displays an anomalous increase in strength. The frequencies and atomic characters of the lattice modes at the center of the Brillouin zone have been calculated for the high-temperature phase for each of these materials. The high-frequency Eu mode does not change in position or character across this series of compounds. Below TN, the Eu modes are predicted to split into features of roughly equal strength. We discuss the possibility that the anomalous increase in the strength of the lower branch of the high-frequency mode below TN in the Sr and Ba compounds, and the weak (silent) upper branch, may be related to the orbital ordering and a change in the bonding between the Fe and As atoms in the magnetically ordered state.