President Uhuru Kenyatta won a second and final five-year term in office and was sworn in as president in November.
Thousands of opposition supporters gathered at Uhuru Park in central Nairobi, chanting slogans and waving tree branches at the symbolic "swearing-in" event, which was organized by Odinga's National Super Alliance (NASA).
In a short speech, lasting less than five minutes, Mr Odinga denounced "election stealing" and the country's "electoral autocracy", but he said little of his future plans.
Mr Musyoka said his home was attacked hours after his police security was withdrawn and he was blocked from attending Mr Odinga's mock ceremony in Nairobi.
Odinga said the vice president would be sworn in at a later date.
Royal Media Services confirmed that Citizen Television, Radio, and Inooro TV were off the air.
Fred Matiang'i, who is also the minister in charge of security, accused some elements in the media of facilitating the "illegal act", putting lives of thousands of Kenyans at risk.
He said the United Nations was urging "that all Kenyan parties, political actors and their supporters maintain a lawful and peaceful social and political environment". "Whenever there is a crisis, there is also an opportunity".
Rotich suggested that clergy and members of the business community could form a "committee that will lead in bringing together all stakeholders at a discussion table".
Numerous protesters were chanting pro-Odinga slogans, waving tree branches and blowing horns and whistles.
Addressing journalists today, Musyoka said they would seek an explanation from the communications body. "So we are very shocked and disappointed that this can happen with no explanation of any kind", Waruru said. "I'm very fed up with this ... government".
"I wish to thank the people of Kenya for the mandate they have given us and for their steadfast confidence in us".
Many of those at the rally had come from the capital's slums.
The swearing-in boils down to Odinga attempting to assert his authority as a political leader, William Atwell, practice leader for Sub-Saharan Africa at emerging markets advisory firm Frontier Strategy Group, told CNBC via email.
The announcement by the National Super Alliance sets the stage for another round of election-related clashes between police and opposition supporters and raises fears of more civilian deaths.
One of the country's main television and radio broadcasters, Citizen TV - which had been covering the event - reported online mid-morning that its transmission had been switched off by the communications authority.
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