Distinguishing between two types of Asheirah - "Asheirah of Moshe" and an ordinary Asheirah: Succah 31b
Considering a tree an "Asheirah" if one sees that the idolaters guard it and don't eat from it, even if one doesn't actually see them worship it: Eruvin 79b-80a
Considering a tree an "Asheirah" if one hears idolaters say, "This is for the intoxicating drink of the house of Nitzrifi," which they drink on their holidays: Eruvin 80a
Benefit from an Asheirah
One may not benefit from the wood: Pesachim 27a, 48a Gideon was permitted to violate the law in using this with an offering, on the night he brought his offering: Temurah 28b-29a Punishment for lighting a fire with this wood, for use: Makkot 22a Punishment for plowing with this wood: Makkot 22a
A Vessel which is fired, to complete its construction, with Asheirah wood: Pesachim 27a
Using the wood to heal a person: Pesachim 25a-b
Sitting on a stool made of Asheirah Wood: Pesachim 27b
Using a palm branch from the tree for Lulav on Succot: Succah 29b, 31b
Using a myrtle branch from the tree for Hadas on Succot: Succah 32b
Using a willow branch from the tree for the Aravah on Succot: Succah 33b
Using a Citron from the tree for the Esrog on Succot: Succah 34b, 35a
Using wood from an Asheirah for a ladder to scale a wall which separates two properties which wish to merge for Shabbat, to permit transportation between them: Eruvin 78b
Using the ashes from an Asheirah: Pesachim 27b; Temurah 34a
Beyond the Legal Issues
It would be appropriate for an arrogant person to be cut down like an Asheirah tree, which is worshipped as an idol: Sotah 5a