The problem with the Social Security Death index is that the person will only be listed if the death benefit was applied for. If he returned to Romania, that is unlikely, though some people did file from abroad.
I find a "John" Mihu in the index, but he died in Ohio, so that would not be the correct person.
Did he arrive in the U.S. before 1924? The Ellis Island database is only for the period 1892-1924. Of the Mihu's on the database, there are four with some form of Johann/János/Joan; they arrived in 1909, 1910, 1912, and 1914 (you said yours arrived after WWI, so after 1919?).
By the way, I notice that many of the Mihu-s on the database are from the village of "Olahdalya".
Do you have any idea exactly what year he arrived in the U.S. and what town he settled in? If some of these other Mihu-s are related, maybe there are some clues there.