Are the vowels “ι, υ, and α” long by nature within a particular word in Greek poetry?

My command of quantitative metre is non existent, but to my knowledge a particular instance of α, ι, υ in a particular word was almost always either long or short: it was a property of the phonology of the word, and not an artefact of the metre.

The quantity of α, ι, υ in word roots is given in larger Ancient Greek dictionaries such as LSJ or DGE. If you scroll through, you will see entries where​ there are exceptions (hence the “almost” above), where one poet once will have used a different quantity for one of those vowels in the stem. Linguists to my knowledge have not treated that as metrical licence, but as linguistic variation: if a poet used the “wrong” length for a vowel, the assumption is that some speakers really were pronouncing it like that.

Again: that’s my outsider linguist impression. Specialists in metre may know better.