Okay, may Lord Papa Ouki forgive me but..... I believe the Renpa Army takes this one.
Renpa and Ouki overall are equals, though I do believe Renpa to be the superior tactician since he supposedly held off both Hakuki and Ouki simultaneously, along with Mougou claiming Renpa is a strategic/instinctual hybrid and I believe Ouki to be the superior dualist since he nearly killed Houken thrice (first time Ouki assumed his death, second and third time Ouki was interrupted) while Renpa was knocked around by Mougou.
These two will lock each other down, they have to. This however works far more in Renpa’s favor since the battle then relies on each General’s subordinates and this is where the Four Heavenly Kings shine.
Ouki has one exceptional subordinate in Tou and a bunch of alright subordinates in his 5 Army Commanders.
The Four Heavenly Kings however, are all exceptional.
Best case scenario for Ouki’s vassals I could conjure (which is still grim) is:
1) Tou vs Kashibou: Tou victory if uninterrupted (highly unlikely), Kashibou stale mates until assistance arrives.
2) Rokuomi and Rinbou vs Rinko: Debatable outcome, most likely stalemate until assistance arrives.
3) Kanou and Doukin vs Kyouen: Kyouen victory, Kanou and Doukin slain.
4) Ryuukoku vs Genpo: Genpo victory, Ryuukoku retreats.
Tou will defeat Kashibou if given enough time. He is a far superior strategist and the Tou cavalry will match Kaishibou’s Guard. Kaishibou himself won’t go down easily and it will take Tou some time to personally kill him, time that Tou doesn’t have.
If Rinko is pincered by the other two in a 2v1 dual, he could lose. However, Rinko is a smart tactician and between his superior Zhao cavalry, his elite guard and his intelligence, he should avoid this. Rinko can defeat either one in a 1v1, however he needs to be fast enough to kill one before the other interrupts. Possible with Rinbou, unlikely with Rokuomi who held against Rinbukun while dodging arrows.
Here is where it all falls apart. Kyouen steam rolls here no contest. Kyouen went up against Renpa, Kyou and Ousen and gave all of them a tough time. His aggressive tactics will crush these two. From here, Kyouen is free to assist whoever needs it and will most likely send troops to Rinko and he himself will ride to Kaishibou’s aid and could kill Tou.
Ryuukoku stands no chance against Genpo’s tactics. He simply cannot match them and as the least combat oriented, he will not punch through Genpo’s lines. The reason this is Ryuukoku’s best matchup is that he will die instantly against any of the other Kings and can at least retreat in this scenario. He will also last longest against Genpo since he himself is focused more on tactics than personal combat.
Considering this was the best outcome I could conjure for Ouki’s vassals, I don’t think I need to state the worst case scenario to show how fucked they are.
From here, Renpa can regroup with his Four Kings and gang up on Ouki with whoever he wants, probably Kaishibou and Kyouen. He is comfortable with doing this since he had no problem planning to gang up on Mougou with himself and Rinko.
I apologise my lord Papa Ouki but I cannot see victory here for you today.