Meloni declared himself president and set up a presidential residence in a blue plastic tent.
The candidate who receives the highest votes in the second round shall be declared president.
Odinga's supporters said he would be declared president at a rival ceremony on Monday, but police banned the event.
He was arrested last month after declaring himself president on the first anniversary of the vote.
In 1956 he implemented a new constitution and had himself declared president for four years.
In 1999 he was declared president for life.
Ohio has gained a reputation as a swing state since the 1980s, and last voted against the person declared president in the 1960 election.
Karzai had already been declared president of Afghanistan.
Joseph Kabila, declared president last week, is expected to be sworn in on Wednesday.
Weizmann was declared president on 17 February 1949.