τίνες ποτ᾽ ἐστέ; πᾶσι δ᾽ ἐς κοινὸν λέγω:
βρέτας τε τοὐμὸν τῷδ᾽ ἐφημένῳ ξένῳ,
ὑμᾶς θ᾽ ὁμοίας οὐδενὶ σπαρτῶν γένει,
οὔτ᾽ ἐν θεαῖσι πρὸς θεῶν ὁρωμένας
οὔτ᾽ οὖν βροτείοις ἐμφερεῖς μορφώμασιν.
Eum. 408-12

Shouldn't ὑμᾶς be in the same case as ξένῳ" " I speak to this stranger... and to you..." Why does the case switch from dative to Accusative.

They should be both in dative. This syntax of lego belongs to the transformation of ancient to modern Greek that started in the classical era.

So the original text has been altered? My biggest problem with translating the Eumenides has been the text itself. It seems like their are alternate versions of the text for many of the lines. Do you know where I can find the most reliable edition of this text.

I didn't make myself clear. The text is not altered. Both Wilamovitz and Murray give the same lines as you wrote them. I just reminded you that modern Greek is not very modern, it starts in the classical era - even modern Greek pronunciation starts at that time (recall Plato's remarks on this change).

What I'm thinking now, is the essence of your question, "why does the case switch from dative to Accusative", what is (at least here) the reason of that transition, even in the very same paragraph!, which in the course of time prevailed?

It is a matter of interpretation and I didn't happen to see some so far. What seems logical to me (and I'm open to any suggestions you may have) is the immediacy of accusative. Aeschylus wanted here Athena turn boldly to Erinyes, and thus he left dative for accusative. Dative is almost as if one refers to an absent person, accusative is stronger and immediate.