Odinga's oath, according to western media, was "I, Raila Omolo Odinga, do swear that I will protect the nation as people's president, so help me God".
Kenya, a key USA ally fighting Islamist extremism in the region, is struggling with deep fractures along political and ethnic lines after a disputed presidential election last August and a repeat election in October.
The supporters say Odinga is their rightfully legitimate leader.
A Senior Lecturer at the Department of Sociology, University of Abuja, Dr Umar Abubakar Kari said, Kenyan leaders should not forget the 2007, crisis in the Rift Valley, where over 1,200 people were reported to have been killed, while thousands others were displaced.
Since the October repeat election and Kenyatta's inauguration, the country has mostly stabilized, with many Kenyans breathing a sigh of relief that the period of political uncertainty had ended.
"A unilateral process of just switching off was not only a violation of media freedom, it was also a violation of fair administrative action, which is expected of any public officers, and runs afoul of Kenya's global and human rights obligations, where Kenya sits as a member of the UN Human Rights Council", said Mr Maina.
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Though Kenya's last election in 2013 was mainly peaceful, the country plunged into widespread violence in the aftermath of the 2007 vote. It followed an August election declared "null and void" by Kenya's Supreme Court over voting irregularities.
Opposition Chief Raila Odinga was expected to visit the home at 11am.
The group said Kenyatta - who has rejected all efforts to engage with his rival - should agree to an audit of the electoral authorities, while leaders should engage on reforms to lower the stakes of political competition. Although heavy police deployment was withdrawn on Tuesday, police used tear gas to disperse supporters. "We are suffering as Kenyans". "This is betrayal in the city for "Jakom" (Raila), how can they abandon him", said one woman wearing a chain of plastic oranges.
But Naftali Muigai, a Kenyatta supporter, said the opposition move was illegal and divisive.
Since independence in 1963, Kenya has been ruled only by leaders from the Kikuyu and Kalenjin groups. Odinga, almost as wealthy as Kenyatta, appeals chiefly to the poor in the Nairobi slums, the Luo ethnic group, and others who regard themselves as marginalized.