Like Jaya said, her language count is five but that is French, English, Spanish, Italian and German. At least according to her official biography on the palace website. She speaks French and English perfectly fluently (When I lived in Paris, I frequented the Café de Flore, where she also went and have
seen her in other places in Paris, though never met her, and heard her speaking both English and French fluently). Whether or not she speaks Italian fluently is slightly debatable (there were some on this forum a while back that said they didn't think Caroline spoke Italian fluently, though I don't know if that is still the case) though Josh Grant, a dancer with Les Ballets Trockadero de Monte Carlo, wrote that Caroline held a lengthy conversation in Italian with one of the other dancers at the dinner after the Dance Forum. Caroline said in an interview with ELLE in the early eighties that she speaks Spanish, albeit "badly" (her words, not mine) though that may have changed and she said in the same interview that she speaks German though we know from when she testified at the beginning of this year that she doesn't seem to speak German with enough fluency for the court.
As for reading Greek and Latin, that is relatively mandatory for all school students in Europe. I did the same when I was at school. You are usually given passages to read and translate in Greek and Latin. And I'm sure that Caroline, being as intelligent as she is, has retained most of that.