Melacha mostly refers to the result not so much to the action. It can be defined as “constructive work”. This is why all melachos shabbos have a physical thing that is created or changed. (besides for hotza’a – which is why it is considered less of a melacha (see Rishonim Shabbos 2a).
Ma’aseh is the actual action of the worker.
Avodah is what one does for another. That is why it is called an Eved and Korbanos are called Avodah – it is done for Hashem.