score:10
It is very probable that your great grandfather was a member of Bund. Bund was a Jewish socialist party. They split from the rest of social democrats in 1903. After the revolution (November 1917) they were disbanded and many of them joined Bolsheviks.
https://en.wikipedia.org/wiki/General_Jewish_Labour_Bund_in_Lithuania,_Poland_and_Russia
I make this conjecture only because you are saying about Jewish background of your great grandfather. In general there were many socialist parties in Russia at that time, and they all wanted to overthrow the monarchy. Some of the most popular were Socialist-Revolutioners (SR) and several varieties of Anarchists. Social democrats (Bolsheviks and Mensheviks) did not play an important role in the revolutions of 1905 or March 1917. There were many people of Jewish descent in all these parties, but my best bet is for the Bund.
Remark. Your expression "Russian Orthodox Jewish" sounds very strange and ambiguous. Does this mean an orthodox Jew who lived in Russia, or a Jew converted to Russian orthodoxy (a variety of Christianity)? The last thing would be very unusual: those Jews who wanted to convert to Christianity usually converted to Lutheranism, not to the Russian orthodoxy.
Upvote:3
You should first read the Wikipedia account of the Revolution of 1905 for the general background of your ancestor's story, and try to see the movie Battleship Potemkin for a dramatic presentation of the events in Odessa. (This movie is a prime example of victors' history, but is a good watch.)
It is not an oversimplification to say that there were many political parties in Russia in 1905 with a variety of subtly different reformist and revolutionary positions, and from your description alone it would be hard to pinpoint which particular faction your great great grandfather adhered to.