Yes -- in Greek, ι, η, υ as well as the combinations οι, ει (and the very rare υι) all sound exactly the same, unfortunately.
A bit like "ee" and "ea" in English: they used to be pronounced differently which is why they are spelled differently, but in the modern language, they are pronounced the same and you usually have to simply learn which one to use where.
All words of more than one syllable in Greek are written with an accent on the stressed syllable.
(Really handy for learners!)
There are no (or few) predictable accent rules in Greek the way that there are in Latin or languages derived from it -- for example, νόμος "law" and νομός "nome" (a kind of administrative entity similar to department/province/...) are distinguished in pronunciation only by accent, as are χώρος "place" and χορός "dance".
Accent in verbs is a bit more predictable but for nouns, the accent can fall on the ending or on the stem and neither of those is more regular than the other. So it's useful that Greeks write the accent always :)
Single-syllable words used to receive an accent in old (pre-1982) spelling as well but that was dropped with the exception of a handful of words.
Sorry, Pascal. What I really meant is why ήτα has a written accent. I wonder if there are some rules for that. The Spanish o the Italian languages, for example, have rules. If you know the pronounciation and the rules of accentuation, you know how to write the word correctly, and the other way round. "este" (Spanish for this) is different from "esté" (he/she/it be). And in Italian: "liberta" (freed female slave, or the verb to free in the present tense) and "libertà" (liberty). In this cases, if the stress is on the last but one syllable (and the word ends in vowel, -n or -s in Spanish) you don't write the accent.