In the Divine Liturgy, I have heard both renderings in different places. For instance, prior to the Creed, in the translation used in my ROCOR parish, the people sing "The Father, and the Son, and the Holy Spirit: the Trinity one in essence and indivisible". Similarly, at the beginning of the Anaphora, we sing, "It is meet and right to worship the Father, and the Son, and the Holy Spirit: the Trinity one in essence, and indivisble". In some other translations blessed for use in ROCOR, I have seen the word "undivided" used.
It seems to me that these words do not mean the same thing. To say that the Trinity is "undivided" means that the Trinity is not divided; to say that the Trinity is "indivisible" suggests that the Trinity cannot be divided.
Is anybody able to shed any light on the nuances of the Greek and/or Slavonic text?
If something is impossible to divide/be divided (indivisible), the state of its being at any given time is that it is not divided (undivided). In the matter of the Holy Trinity, to say that it is indivisible, is to acknowledge that is undivided.
OTH, to say that it is undivided, does not necessarily mean that it is not indivisible. At first glance, this is problematic, but if you think about it, you are talking about an entity that exists in an undivided state eternally--in the past, now and in the future. Therefore, I would think that the difference between the two terms is not significant as a practical matter.