The main types of public transport in Odessa are trams, trolleybuses and minibuses ("marshrutka").
It is not common for drivers to speak English. So, unless you speak Russian or feel adventurous, avoid public transport. Once you're in the city center, virtually everything you need (lodging, cafes and restaurants, places of interest, and the hackathon venue) is within walking distance.
Be careful when you wait for the luggage. It doesn't come on a classical baggage carousel. Instead you have to wait on the STREET in front of the airport for the airport truck.
As soon as you exit the customs, there will be lots of taxi drivers asking you if you need a taxi. Their prices are VERY high and they basically rip tourists off, so do not agree. The normal ride to the city center should not cost more than 60 UAH. It's better to call one of the taxis under the phones below.