A Budapest native, Ordassy received her diploma from the Budapest Academy of Music in 1947; that same year she also won second prize (behind Victoria de los Angeles) in the International Music Competition in Geneva. Ordassy continued her studies with Gina Cigna at the La Scala School in Milan and made her professional debut in 1950 as the Second Lady in La Scala's Die Zauberfl‹te, conducted by Otto Klemperer.
Ordassy emigrated to the U.S. and won a scholarship and a Met contract on the 1956 "Auditions of the Air" radio series, according to Opera News. She made her Met debut as Gerhilde, one of the Valkyries, in Die Walk‹re in 1957.
She sang Alisa in 118 Met Lucia di Lammermoors and 109 Giovannas in Rigoletto. Other frequent Met roles included Ines in Il trovatore (the part in which she made her final appearance wih the company in 1977); Cura in La forza del destino; the Priestess in Aida and Clotilde in Norma.