In the same year the Budapest audience could attend Erkel's Hunyadi László in a new production, in which Osváth sang the role of Mária Gara. She had such outstanding success that in 1937 Toscanini engaged her to sing the Queen of the Night at the Salzburg festival. She began as a Mozart performer and sang the leading roles of all the Mozart operas performed in Budapest (Queen of the Night, Pamina, Donna Anna, Fiordiligi, the Countess, Konstanza). She began singing dramatic Wagner roles (Elza, Eva Pogner) at the end of the thirties, surprisingly with immediate success. It was from this time onwards that her real stage art flowered; in essence this was a triumph of instinctive genius. She exuded the air of the given role as soon as she entered the stage, and being a lyric personality, easily found the way to the audience's hearts.
She was a witness to and participant in historic moments: she sang in the Bánk Bán production in which (on the basis of the revision by Miklós Radnai and Nándor Rékai), lacking a suitable tenor, the role of Bánk was given to the baritone Imre Palló. Osváth also sang in the 1953 production of Bánk Bán, in which a return could be made to the tenor Bánk, as the Opera once again had a suitable singer in the person of József Simándy.
The series of post-war performances opened on 15 March, 1945, with the second and third acts of Bánk Bán, with Júlai Osváth's participation. In this spring the repertoire was put together on the basis of a singular principle: whatever there were sets and props for. They played – with full houses – The Land of Smiles, Die Fledermaus, and János vitéz, with Osváth – and Júlia Orosz, János Sárdy, Imre Palló, Oszkár Maleczky.
In 1946, when under the direction of Aladár Tóth the Mozart revivals continued with Don Giovanni, altered in many places by Kálmán Nádasdy, Júlia Osváth was technically even better than ever before. She sang Donna Anna with light naturalness; she came to be regarded as the embodiment of the singer-actress, whose acting can hide the fact that in the meanwhile she solves tasks in singing that others find a problem.
The Mozart cult associated with the name of Klemperer grew to never before seen proportions in the fifties, when – and for a long time afterwards – Osváth was the only real Pamina and Countess on the Hungarian opera stage.
She was the Hungarian Figaro-Countess, the Hungarian Marschallin. But it was not only the high-toned roles that she was at home in: there had never been a more provocative and more ordinary, in other words a more genuine Musette on the Opera stage. She gave excellent performances as Erkel heroines, and was a splendid Desdemona and Elisabeth in Don Carlos. Her singing in the only production of lasting value of the post-1949 expansion of the repertoire, the spectacular-lyric, highly successful 1951 revival of Onegin, was also of lasting value. She was a permanent member of the Opera, and was awarded the Kossuth Prize and the title, Outstanding Artist.