Speech and vocal sounds are at the core of human communication. Cortical processing of these sounds critically depends on behavioral demands. However, the neurocomputational mechanisms enabling this adaptive processing remain elusive. Here we examine the task-dependent reorganization of electroencephalographic responses to natural speech sounds (vowels /a/, /i/, /u/) spoken by three speakers (two female, one male) while listeners perform a one-back task on either vowel or speaker identity. We show that dynamic changes of sound-evoked responses and phase patterns of cortical oscillations in the alpha band (8-12 Hz) closely reflect the abstraction and analysis of the sounds along the task-relevant dimension. Vowel categorization leads to a significant temporal realignment of responses to the same vowel, e.g., /a/, independent of who pronounced this vowel, whereas speaker categorization leads to a significant temporal realignment of responses to the same speaker, e.g., speaker 1, independent of which vowel she/he pronounced. This transient and goal-dependent realignment of neuronal responses to physically different external events provides a robust cortical coding mechanism for forming and processing abstract representations of auditory (speech) input.