About 70 more people are being treated in hospital and there are fears that the death toll could rise further.
Residents of villages close to the city of Cuttack fell ill after consuming alcohol spiked with chemicals used in the manufacture of some medicines.
Deaths from contaminated alcohol are a regular occurrence in India.
The Orissa government has ordered a judicial investigation into the incident and nine people, including eight liquor sellers, have been arrested.
The illegal alcohol - commonly called desi daroo or country-made liquor in India - usually costs as little as 10 rupees (20 US cents) and the majority of the consumers are poor, daily-wage workers.
The tainted liquor can lead to fits, vomiting and death.
Orissa has witnessed many incidents of toxic alcohol deaths.  Nearly 200 people died in Cuttack in 1992 after consuming a deadly combination of methyl and ethyl alcohol. In 2009, 33 people died in two separate incidents in Khurda district after consuming country liquor.
It is a wider problem across India too:
Correspondents say that Gujarat has taken the strongest action on toxic liquor with a new law making the illegal manufacture and sale of toxic alcohol there punishable by death. It says the law was intended to deter those involved in the illegal trade.
Gujarat, Mizoram and Nagaland are the only states in India where alcohol is totally prohibited by law.
The number of people who have died in the Indian state of Orissa after drinking toxic illegal alcohol has risen to 31, officials say.