twins who won an oscar?

The Only Twins To Win Oscars: Julius J. Epstein and Philip G. Epstein, 1943. (With Howard Koch, they scripted that year's winning screenplay Casablanca);
Christoph Lauenstein and Wolfgang Lauenstein, 1989. (They produced the winning animated short film, Balance.)

I believe Joel and Ethan Coen won for Fargo.

Ceili: Joel and Ethan Coen won the 1997 Oscar for best original screenplay (Fargo), but they are not twins: Joel was born in 1954, Ethan was born in 1957.