Only credit cards that Odessa and other Ukrainian banks operate with are Visa, MasterCard and EuroCard.
Many banks also operate with traveler's checks.
For cashing credit cards and traveler's checks you will need your travel passport. Other credit cards, such as American Express, Discovery or Diners, are not accepted in the Ukraine. There are no problems with cash exchange in Odessa like anywhere else in Ukraine - exchange booths are scattered all around, many of them work till late night. US dollars, German Marks and Russian Rubles are exchanged by majority of exchange booths. But some of them operate with many different, up to 25, stable currencies.