None of the Oni dice are necessary to play the game--including the initial set of 10 at the Deluxe backer level. Even the retail-level pledge includes all the dice you could possibly need to play the game.
That said, having two different tones of dice can help better organize your game space. Designating the black dice for the Oni's attacks is one way this can help.
By the rules, the Oni does not roll more than ten dice at once. However, certain Oni (like the Ketsueki Oni) can go berserk and roll even more than that.
Furthermore, certain game effects allow you to roll a certain number of dice as part of their resolution (like Battlefield Tactics, which allows you to roll four dice and share them with other players). A second color of dice can be helpful here to remember which dice have been designated for different things.
In summary--the Oni dice aren't essential, but they're convenient.