Yuuji doesn't have a soul
To understand my theory to why Yuuji has no soul, we need a basic understanding of Mahito's cursed technique. Idle Transfiguration gives the user the ability to change the shape of a persons soul when they "touch" it. By changing the soul's shape, the body has to morph to adapt. That should be enough info for now, let's get into it.
At the start of their fight, Mahito mentions how Yuuji hit his soul when he punched him. He then theorises by saying that it is possible because Yuuji's body harbors two souls instead of just one.
However, when Mahito touches Yuuji and activates Idle Transfiguration, something unexpected happens: instead of accessing to Yuujis soul and transfiguring him, he ends up in Sukuna's Inner Domain, where he is told not to touch Sukuna's soul a second time or else.
Now it gets tricky.
According to Mahito, Yuuji's body hosts two souls. Having hold one of Sukuna's fingers before, Mahito should be able to tell the difference, especially since Sukuna is a curse and Yuuji is a human (as far as we know).
So why did he touch Sukuna's soul instead of Yuuji's?
There could be two possibilities: the first one is that Sukuna hides Yuuji's soul in his Domain, so when Mahito touched it, he faced Sukuna. But that doesn't make sense to me, because then Sukuna could have just destroyed or overwritten Yuuji's soul and taken over.
The second possibility is that Yuuji originally had no soul. We know that cursed energy is produced by the souls (which is why sorcerers are more resistant to Idle Transfiguration than regular people), but apparently, Yuuji had no cursed energy at the beginning (don't get me wrong, Maki and Toji both have a soul, it just doesn't make CE, but a soulless being will never make CE), as Megumi mentioned (he was wondering wether or not Yuuji was like Zenin-senpai/Maki or not).
When Yuuji ate the first finger, Sukuna's soul nested itself into Yuuji. Normally, that would mean that Sukuna would take over and bam, the end, but that was not the case. In fact, Yuuji could quite easily suppress Sukuna from the beginning, and I think that's because Sukuna's soul just placed itself where Yuujis soul normally would have been.
The reason why Yuuji would have struck Mahito's soul is because he is more or less aware of what a soul feels like, since he spent most of his life having none and then suddenly harboring one.
So in short: Yuuji's body was like an empty soul receptor and he received Sukuna's. Since it doesn't "overflow", he is able to keep control. He is aware of what a soul feels like and is able to injure them.