From 1945 until 1949, Oberhuber studied sculpture at the Federal school for arts and crafts, Innsbruck. In 1948 he made his first attempt to use texts as ‘image value’. 1949 saw the beginning of informal painting and the founding of informal sculpture. Informal sculpture was replaced by so-called ‘scrap sculpture’ made of ‘useless’ material. Both his text pictures and furniture sculptures should be emphasised. From 1950 until 1951 he studied at the Academy for Fine Arts in Vienna under Fritz Wotruba and at the same time he also studied under Willi Baumeister at the Federal Academy of Fine Arts in Stuttgart. In the mid 1950s, Oberhuber turns to representational painting.
He is said to be one of the most glittering personalities in Austrian post-war art. He was an active gallery owner, university professor and vice-chancellor, painter, draftsman, sculptor, stage designer and furniture and fashion designer. At the end of the 1950s, he announced the ‘Theory of permanent alteration’. In this context he started to reject the formation of any kind of style. Since then he holds on to his principle and is active in various different fields.
In the mid 1960s he created a series of Zahnbilder (tooth images). From 1964 until 1965 he worked together with Hans Hollein, Walter Pichler and Gustav Peichl as an editor for the architectural magazine “Bau”. In 1972 he participated in the Biennial in Venice. Oberhuber was friends with Monsignore Otto Mauer of Galerie nächst St. Stephan gallery, Vienna. In the 1970s (1973-1978) he became artistic director of this gallery. In 1977 he participated in Documenta 6, took over a professorship at the University for Applied Arts in Vienna before becoming its vice-chancellor (1979- 1987; 1991 – 1995).
In 1983 he exhibited his work at Albertina in Vienna. In 1982 he again took part in documenta7 in Kassel. In 1990 the artist received the Austrian federal award for foreign culture and the regional prize for art of the Region of Tyrol. In 1999 he became honorary member of the Wiener Secession, where he also exhibited in 2006. In 2004 the artist received the Austrian cross of honour for science and art. In 2009 his work was shown at Österreichische Galerie Belvedere gallery in the single exhibition “Die Leidenschaften des Prinz Eugen”.