Rakata Empire, Eternal Empire, Old Republic and Sith Empire vs Yuuzhan Vong

Each respective factions are at full power. Assume everyone has great synergy. 

Does it include the certain members of the factions such as Soa, Valkorion, Shimrra etc.?

Yes

The team, and handily at that.

Team absolutely obliterates. SF + Soa + Valk + Gravestone + other shit already give them a dominant edge. The fledgling GA was able to gain an edge, and there's no reason these guys can't, especially since they're likely superior in force users and other stuff compared to the GA (Luke being the only exception, though I feel Valk is close).

Team fingerstomps

Honestly, take out Valk and all of the other major FUs on the team and they still stomp. Far greater numbers and better tech (eternal fleet, the Silencers, etc).

team