What version of the bible do Greek speaking Christians use? Do Greek speaking Christians still use the Septuagint and original New Testament text? Or do they have a "modern Greek translation"? I ask because the New Testament is 2000 years old, presumably the Greek language has changed and evolved a lot in that time and so the original NT might not even be understandable to a modern Greek speaker.

I'm interested in what Greek speaking Christians use in general (Catholics, Orthodox, Protestant), but I'm also very interested in the Greek Orthodox church in particular. I'm curious what version of the scriptures they draw upon in their liturgy: the originals? or a modern paraphrase/translation?
The language has certainly changed. As such, translations into modern Greek are used.
Today's Greek Bible is often used, and translations by the Hellenic Bible Society have the Blessing and Approval of the Ecumenical Patriarchate, the Holy Synod of the Greek Church and the Patriarchates. There are other translations of the Bible into modern Greek, and it must be noted that the underlying manuscript(s) used vary just as they do in English translations, but perhaps more so because of Greek Orthodox distinctions. Going beyond this into the realm of what every Christian group in Greece prefers is too broad. Given that Eastern Orthodoxy is the predominant Greek religion, I've stuck to this.
The history of translating the Bible into modern Greek is fascinating and filled with lots of controversy, but such a review is beyond the scope of this answer. I refer you to this Wikipedia article for some additional context, but it is quite biased and often unsourced. The Greek version has a list of translations.
The type of Greek used in Divine Liturgy varies by jurisdiction and local conventions. Increasingly, Greek Orthodox churches use the predominant language of the country where services are held. Where Divine Liturgy is in Greek, it is often a mixture of modern and biblical (Koine) Greek (similar to how English-speaking churches retain some archaic English phrases in their liturgies).