I seem to recall that holding the Oracle under the Romans (who have their own culture in EB) gave a positive effect for happiness. But for all their Greek bashing, the Romans were increasingly hellenised throughout our time period, so you can imagine that the Greeks under Roman rule wouldn't mind much.
The barbarian culture (as celts rather than germans) did actually sack Delphi just before the start of the EB time period, and the Greeks naturally made a big deal of this in their writings. The Delphic oracle had previously been extremely important in guiding and uniting Greek states culturally. At least in myth and the kind of 'just so' history that was popular amongst ancient writers.
As such, you can reasonably expect an oracle (an elderly priestess by the way) under barbarian rule to be screaming hate and dire warnings about the anger of the gods. If you want to stay in the area, end the oracle and tell tales in your halls about a monstrous woman who cast spells from her cave. If it's just a raid, leave the oracle alone (it has already been sacked) and plunder the temples.
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