Unlike the other three, Gokuu isn't a reincarnation of a celestial being. He's the same Gokuu that was formed from the concentrated aura of the earth and birthed from a rock centuries ago. He's thus neither truly youkai or human, but generally considered a bit of both. In his natural form of Seiten Taisei Son Gokuu 'the great sage equal to heaven' Gokuu possesses seemingly infinite and invincible power, but is also an insane killer unable to tell friend from foe. (He's also totally gorgeous, if you go for long-haired wordless smiling psychopaths.) At some point in the past his power was contained by the diadem that he wears, which seems to have turned him into just an ordinary adolescent monkey. The diadem itself is a special controlling device, different from the usual kind that youkai use to restrain their power. It's a concatenation of divine energy, god-manufactured, which it has to be to contain the kind of power Gokuu has. 
It's twice come off in the manga, leading the divine Gokuu to go after Gojou and Sanzou as well as the enemy of the moment. One time it was restored by the direct intercession of Kanzeon, and once by Sanzou reciting the Maten sutra. Returned to his senses, Gokuu was naturally crushed at what he'd done.
Five hundred years ago Gokuu was brought up to heaven by some kind of heavenly trader where he made the acquaintance of Sanzou's former incarnation, Konzen. What happened afterwards we don't yet know. Gokuu did something for which he was punished by being imprisoned in a cave on top of a mountain, alone, and the memory of what he did was taken from him. All we know is that it had something to do with Konzen, and something to do with a desire not to lose Konzen. (Gokuu canonically hates people having secrets from him. 'I don't have secrets, it's not fair for him to,' he says, apropos of Gojou's secrecy about his half-brother. One could point out that Gokuu has no secrets in his past because he has no memory of his past, and that of all the characters he's possibly the greatest enigma.)
At any rate, he remained on his mountain top, longing for the sun that he couldn't see, and terribly lonely, until the young Sanzou on his travels heard Gokuu's 'voice' calling him. It was so persistent and so annoying that Sanzou had to go find him, with the stated intention of knocking his block off. 'But when I saw him he looked at me in such a dumb-ape fashion that I just sort of forgot about wanting to hit him.' Sanzou stretched out his hand to Gokuu and Gokuu's chains fell off him. Sanzou brought him back to the capital where the other monks treated him with the same contempt and dislike the monks of Sanzou's youth had shown Sanzou. This served to cement the relationship between Sanzou and his young pet.
Gokuu is about eighteen in this series, and like most eighteen year olds, and most Son Gokuus, he's always hungry. And always telling people about it. A real whiner at times. It's not surprising Sanzou prefers to room with Hakkai. As a character Gokuu's the embodiment of a couple of untranslatable Japanese words and concepts. Pure-hearted, straightforward, 'bright'-- all suggestive of innocence and a transparent nature with no dark emotions and nothing to hide. Probably what Sanzou would like to be, if he weren't such a complicated mess. His devotion to Sanzou is complete, and hints are that Sanzou is attached to Gokuu in his fashion. Only being Sanzou he expresses that by calling him 'bakazaru' (stupid monkey) and hitting him over the head with a harisen (folded piece of white paper used, as far as I can tell, for hitting people over the head with in stooge comedy.) That seems to be just fine with Gokuu. We're definitely not dealing with New Age men here. Nope, the most tongue-tied of otoko-rashii (manly) Japanese guys for us, who show deep feeling by hitting people and calling them names. Heigh-ho. So the fact that Gokuu and Gojou are always fighting there in the back of the jeep that's taking them to the west, and always trading insults the rest of the time, probably means they're the best of friends. Easier to take is Hakkai's relationship with Gokuu, which the Japanese fen have characterized as 'maternal.' Looks after him, fusses over him, gives him encouraging words of advice. Hakkai's good with kids, what can one say?