1. The "God-fearing Greeks" would have been using Koine
From the Baker Encyclopedia of the Bible, Koine Greek - the Greek in which Paul wrote and presumably preached, was the lingua franca. It says:
Hellenism and the Koine Dialect. The conquests of Alexander the Great encouraged the spread of Greek language and culture. Regional dialects were largely replaced by Hellenistic or koine (everyday) Greek. That language is known through thousands of inscriptions reflecting all aspects of daily life. The koine dialect added many vernacular expressions to Attic Greek, thus making it more cosmopolitan. Simplifying the grammar also better adapted it to a worldwide culture. The new language, reflecting simple, popular speech, became the common language of commerce and diplomacy. The Greek language lost much of its elegance and finely shaded nuance as a result of its evolution from classic to koine. Nevertheless it retained its distinguishing characteristics of strength, beauty, clarity, and logical rhetorical power.
It is significant that the apostle Paul wrote his letter to Christians in Rome in the Greek language rather than in Latin. The Roman empire of that time was culturally a Greek world, except for governmental transactions.
Robertson, in his Grammar continues the theme saying:
The spread of the Ionic over the East was to be expected. In Alexander’s army many of the Greek dialects were represented.8 In the Egyptian army of the Ptolemies nearly all the dialects were spoken.9 The Ionians were, besides, part of the Greeks who settled in Alexandria. 1 Besides, even after the triumph of the Attic in Greece the Ionic had continued to be spoken in large parts of Asia Minor. The Ionic influence appears in Pergamum also. The mixing of the Attic with foreign, before all with Ionic, elements, has laid the foundation for the κοινή.2
In short, if Alexander the Great (a Macedonian) was using classic Greek as opposed to his own dialect, then it is safe to assume all the "God-fearing" Greeks were using the same.
2. The Jews would have been conversant in Greek, but would have spoken Aramaic in the synagogue
Acts 21 records the languages in which Paul spoke. It says:
37 As the soldiers were about to take Paul into the barracks, he asked the commander, “May I say something to you?”
“Do you speak Greek?” he replied. 38 “Aren’t you the Egyptian who started a revolt and led four thousand terrorists out into the wilderness some time ago?”
39 Paul answered, “I am a Jew, from Tarsus in Cilicia, a citizen of no ordinary city. Please let me speak to the people.”
40 After receiving the commander’s permission, Paul stood on the steps and motioned to the crowd. When they were all silent, he said to them in Aramaic[a]:
From the UBS Handbook, the entry on Acts 21:40 says:
Although almost all translations say that Paul spoke to them in Hebrew, actually Paul would have been speaking in Aramaic, the language which the Jews of that day used (see NEB “in the Jewish language”). Spoke to them in Hebrew may be rendered as “spoke to them; the words he used were Hebrew words,” “spoke to them, using the Hebrew language,” “spoke to them in their own Jewish language,” or “…in the language used by the Jews.”
Paul was probably not alone in speaking both Aramaic and Greek, the way much of the world speaks both their own native tongue, plus English in order to understand much of the dominant world culture in which they live.
tl;dr> Most likely, they spoke different languages at home, but a common one when together.
