Well, Odesa is just across the Akkerman Gulf and the Romanian border, so Romania could realistically occupy it, but the main issue is that it would have to enter the Russian Civil War, which it had no interest to do. For the sake of the question, let's say it is emboldened by the Khotyn Uprising and Allied pressure to secure Odesa. What would change? Not much. Part of the Russian population would leave(maybe some Whites would be allowed), some Romanians would come, but overall it would not become a Romanian city due to the high Russo-Ukrainian population and it would only be exploited as a port.
After WWIII, the USSR gets Odesa back and the interwar years remain fir the city a period of Romanian adventurism.