The play Oedipus Rex by Sophocles was composed in approximately 430 B.C.E., that is some 430 years before the birth of Jesus. Thus there is no way in which Christianity could have influenced Sophocles. It is also highly unlikely that Sophocles would have been familiar with Judaism; we have no record of his travelling outside Greece and no evidence of familiarity with Hebrew. In general, during this period, Athens was extremely insular, and even philosophers such as Plato and Aristotle have only very superficial familiarity with cultures other than their own (mainly Persian and Egyptian).
The Bible does not mention Sophocles nor is Sophocles part of the Christian tradition in the way the Virgil, Ovid, Plato or Aristotle became assimilated to Christian education in the middle ages; medieval readers would have known Sophocles mainly third hand via Herman the German's middle commentary on Aristotle's Poetics. Christian writers in the early modern period did read Sophocles, and he became widely admired. It is possible to read Sophocles through the lens of Christian morality, just as it is possible to use Christian moral principles to judge any work or act, but there is no direct relationship between the two.