I looked into this a few years ago and though I can't really offer any verified sources on the matter, there is, or at least there was, quite a bit of information on Japanese Wikipedia.
So firstly, the Chinese influence. It is pretty established that he did train in Byakurenmon-ken and Giwamon-ken. He supposedly was also given some kind of grandmaster rank in at least one of these two but what that title really means is for me a bit unclear. It doesn't necessarily mean that he inherited the art and became its big kahuna but might just mean a license to teach, kind of like a menkyo. There is not a lot left of these styles so we cannot really see the influence they've had on what became Shorinji Kempo.
For the Japanese influence, Kaiso was raised for several years by his paternal grandfather, So Shigeto. He was a renowned martial artist specializing in kendo and sojutsu. But he was also allegedly very proficient in koryu jujutsu, most likely Fusen ryu. I see that this information is now on English wikipedia, it wasn't a few years ago when I found this on the Japanese site. Might even have been me who added it to the English site but it was more than ten years ago so not sure.
As for the Hakko ryu influence, this is what I believe are my own words on wikipedia:
Many sources claim that Doshin So trained in Hakkō-ryū Jūjutsu and that techniques from there was incorporated in Shorinji Kempo. However, the Shorinji Kempo headquarters has no records of this and the records of the Hakkō-ryū organization merely show that he sat in on a few sessions. Any implication that Hakkō-ryū may have had on Shorinji Kempo would have been very minor since he got back to Japan in 1946 and Shorinji Kempo was founded the following year (Hakkō-ryū was founded in 1941 when Sō was still in Manchuria).
I personally believe that the koryu jujutsu training that he got from his grandfather is the core of Shorinji Kempo. You can find some Fusen Ryu clips on YouTube where you'll see some similarities.
Sorry about not being able to offer any verifiable sources but hopefully it sorts out some questions at least.
Peter Thorvald
Shorinji Kempo
Sweden