In an ancient Greek play, what word would we use to refer to the different acts? Μέρος? Λόγος?
Woodhouse doesn't seem to have anything relevant under the noun "act."
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Ancient Greek plays weren't exactly divided into "acts" in the modern sense; they had a more complex structure, based largely on alternation between dialogue scenes and choral odes. A basic description of the overall structure of a tragedy can be found, for example, here (under "Divisions of a play").
[ETA: as C.M. Weimer points out in comments, comedy had a somewhat different structure, so this may be less directly relevant to your specific question about Menander's Dyskolos.]
The main elements, in order, were:
Most of a play consisted of an alternation between episodes and choral odes. Of these terms, ἐπείσοδος is probably the one that's closest to our modern "act", especially in the fourth century BC and later when the number of episodes was standardized to five.
(Note that πάροδος, ἐπείσοδος, and ἔξοδος are all feminine nouns since they're based on ἡ ὁδός "way, road".)
This edition of Dyskolos has labels like Μέρος B' (at line 233), so it looks like the best word for this would be μέρος. However, this may be a matter of a modern editor shoehorning things into a modern structure.
The edition by Jacques has divisions like "Acte II, scène 1," in the French text, but in the Greek text on the facing page there are no such labels.
What seems to happen is that we get a dramatized scene with dialog, then the chorus comes on stage, and the scene ends. This seems to confirm TKR's speculation in comments that each "scene" is an episode plus an ode.