So basically, the (likely/somewhat plausible) options are:
1) Someone in the Order, but not working under Sanctus or Agnus (possibly before they came to power), created Nero as a "replica" of their Savior
(If we exclude the novel, we don't know how long Sanctus was in power. If his predecessor was as nuts as he was, then there's no reason why that predecessor's research couldn't have been hidden from Sanctus. If we do include the novel, then Sanctus came to power by poisoning his predecessor and probably then proceeded to eliminate his most loyal followers, who may have in a fit of spite hidden the result of their research - Nero - from Sanctus.
(And on that subject, was Sanctus ever actually surprised that Nero had Sparda's blood? As far as I remember, he just says that he wanted to use Dante, who is stronger, but Nero will do fine. This may have been the backup plan all along. In that case, the only one who didn't know but should have is Agnus. Maybe Sanctus didn't trust him all that much after all and maybe Agnus hadn't been "in on things" when Nero was created 16-ish years ago.)
2) Nero is a descendant of Sparda through another human woman an unknown number of years in the past
(This would mean he's got less demon blood than Dante. I personally don't feel that claims that he's weaker than Dante are accurate. Remember, we should be measuring him up to DMC3 Dante, who faced a very similar challenge - a human who became a demon and then tried to gain Sparda's power. Also, everyone - absolutely everyone - needs a special weapon to trigger, usually a Devil Arm, but also Rebellion and Yamato. Nero doesn't have one of those until Yamato. I know people complain about Nero's lower regen rate, but we don't actually know if it is lower. The one time we see him injured in a cutscene, those lances are left inside him for most of the time.)