I didn't really think about Kamui's berserker mode, but I'll go with him not having it.
Sougo did seem to be around Kamui's level (although he seemed slightly on the back foot, but with a stronger sword this might not have been the case). Sougo seems around Gintoki's level too, going by the Excalibur arc where they were even until Gintoki's sword gave out, whereas Hijikata seems significantly weaker than Gintoki judging from their short fight. Kondo is definitely weaker than that, but it's unclear how much by, since he never has proper fights, but he was far less impressive against the Yato than Hijikata.
Sougo can keep Kamui busy, but considering Kagura totally dominated Abuto, who was vastly more experienced in combat than her, unless Hijikata and Kondo are at least in her ball park of strength they seem screwed. Kagura's been shown to catch bullets and lift huge boulders, which are the kind of feats Hijikata's never matched (and Hijikata was shocked when another character threw a boulder in the Yagyuu arc). It's hard to see him and Kondo holding up for long any longer than Abuto did, considering the strength difference.
Plus, if it played out with Kamui attacking Hijikata first and Kagura stalling Sougo (which would probably just be luck, since I doubt she'll strategise), things could whittle down to 2 vs 2 very quickly.