Which part of the Avesta is considered the oldest?

The Gathas are considered the oldest part of the Avesta.

The Gathas are a collection of 17 highly archaic hymns in Old Avestan, traditionally attributed to Zarathushtra, or Zoroaster. They form the innermost and oldest layer of the Yasna, the principal Zoroastrian liturgical text. Although the Avesta as a whole contains material composed over several centuries, the Gathic language is generally regarded as older than the Young Avestan language used in most surviving sections.

The hymns address Ahura Mazda and explore themes including truth or asha, moral choice, prayer, and the conflict between beneficent and destructive forces. They were transmitted orally for centuries before being written down, so the age of the surviving manuscripts is much later than the age of the compositions. The 17 hymns are arranged in five groups and occupy Yasna chapters 28–34, 43–46, 47–50, 51, and 53. Yasna is the larger liturgical collection containing them, not the more precise answer to this question; the Vendidad and Yashts are generally later textual layers.