Aegean has bought the Olympic Air after the European Union cleared the purchase (read more here) and now you can earn and burn Miles&Bonus miles on Olympic Air flights.
Aegean Miles&Bonus member have been able to earn tier miles on Olympic Air flights starting on February 1, 2014, and the redeeming miles have been possible since February 11, 2014.
You can access Aegean’s chart of earning miles here and burning here.
Conclusion
The Olympic Airlines is not part of Star Alliance, although it is owned by alliance member Aegean. Members of other Star Alliance frequent flier programs are not currently able to earn or redeem on Olympic Air flights.