The Swaraj Party was officially formed on January 1, 1923, by C.R. Das and Motilal Nehru after the Gaya session of the Congress. The party emerged as a response to the suspension of the Non-Cooperation Movement, with the strategy of contesting council elections and disrupting colonial governance from within. The other options (March, April, May 1923) are incorrect as the party was formed specifically in January 1923.