Educated in Budapest, he emigrated to Austria in 1956, where he studied at the Vienna Music Academy.

Born in Budapest, Erőd studied at the Franz Liszt Academy of Music with Pál Kadosa (piano) and Ferenc Szabó (composition).

He emigrated to Austria in 1956 and studied there at the Vienna Music Academy, with Richard Hauser [de] (piano) and Karl Schiske (composition).

[1] He took several summer classes at the Darmstädter Ferienkurse, studying with Eduard Steuermann and Luigi Nono.

[2] His students included Georg Friedrich Haas,[1] Gerhard Präsent and Johannes Maria Staud.

[1] He married in 1969 and had five children, among them Adrian, a baritone, and Leonard, a bassoonist at the Vienna Radio Symphony Orchestra.

[1][5] Stylistically, Erőd's music was initially influenced by Hungarians such as Béla Bartók and Zoltán Kodály.

Before his emigration and during his studies in Vienna, he was interested in the dodecaphony of the "Second Viennese School", and serialism.

He began composing his second opera Die Seidenraupen (The Silkworms) in 1964 and completed it in 1968, when it was successfully premiered during the Wiener Festwochen at the Theater an der Wien with singers Jeannette Pilou and Oskar Czerwenka.

[6] The composer describes the work as being based on three scales, for the three main characters, which are derived from each other and sometimes combined in a way leading to tonality.

[3] He dedicated Milchzahnlieder (Baby Tooth Songs) for soprano and chamber orchestra, Op.

Cologne Opera presented the first performance in Germany in February, 2021, following COVID-19 protocols required at the time.

He composed lieder, such as Canti di Ungaretti (1988)[2] and "Vier Gesänge" Op.