The production started in 1959–1960. Models 1001, 1002, 1003, 1013, 1103, 1204 were of original Polish construction. Models 1304 and 1305 were functional counterparts of ICL 1905 and 1906 due to software agreement. The last model was 1325 based on two models from ICL.
The name comes from the Odra River that flows through the city of Wrocław
The computers were built at the Elwro manufacturing plant, which was closed in 1989.
ODRA-1002 were capable of only 100-400 operations per second.
In 1962, Witold Podgórski, an employee of Elwro, managed to create a computer game on a prototype of ODRA-1003; it was an adaptation of a variant of Nim, as depicted in the film Last Year at Marienbad. The computer could play a perfect game and was guaranteed to win. The game was never distributed outside of the Elwro company, but its versions appeared elsewhere. It was probably the first Polish computer game in history. 
The operating system used by the ODRA-1204 is called SODA. It was designed to work on a small computer without magnetic storage and can run simultaneous loading and execution of programs.
Up until 30 April 2010 there was still one ODRA 1305 working at the railway station in Wrocław Brochów. The system was shut down at 22:00 CEST and replaced with a contemporary computer system. Few Odras are placed on exhibition in museums and at least one is still operational and maintained by students of electrical school which created a fan club around the machine.
- Bronisław Obirek "Maszyny analityczne organizacja zmechanizowanego obrachunku" Wydawnictwo Naukowo Techniczne, Warszawa 1970 r.
- Kluska, Bartłomiej; Rozwadowski, Mariusz (2011). Bajty polskie (in Polish). Łódź: Samizdat Orka. p. 6. ISBN 978-83-927229-1-5.
- Jacek Bomersbach (25 April 2008). "Zabytkowa Odra pracuje na stacji kolejowej" (in Polish). Alert24.pl. Archived from the original on 30 May 2008. Retrieved 26 April 2008.
- "Wyłączono ostatni komputer Odra w Polsce!".