IIRC Hidden Power's junk is determined when it's used, not learned. So there's no way to do this unless, as I said, you were to change the pokemon's core stats mid-battle (which is obviously not happening legitly).
To elaborate on this, Hidden Power's type and base power are dependent on the IVs of the Pokémon using them,
at the time of use.
Here's an Unown:
[FixedIVs] Unown.100 "H" @ Insert Choice item here
- Hidden Power
Assume this Unown is legit, and its Hidden Power is of the Dragon type with a base power of 55. If also playing legit, all uses of the move by that Unown will be Dragon-typed, 55 power.
Next, assume you're modifying that Pokémon for use in legit battles.
[FixedIVs, Illegal] Unown.100 "H" @ Optional Insert Choice item here
- Hidden Power
- [Illegal] Hidden Power
- [Illegal] Hidden Power
- [Illegal] Hidden Power
All instances of that move on the same Unown will have the same type and base power, Dragon and 55, because they use the IVs of the user. I'm not sure whether choice items block duplicated moves in illegal movesets, but all Hidden Power instances behave the same; it would only matter if you wanted the extra 45-72 PP
Finally, assume you're using the modified Unown for use in cheated battles. Turn on your cheat device and you can change your Unown's IVs mid-battle, which might not actually be broadcast to your opponent. These would change the type and the base power of any and all Hidden Powers on the user.
The battle may run oddly in that case, though. If the type changed, you may see "It's super-effective!" and the defending Pokémon fainting, but the opponent would see "It's not very effective..." and their Pokémon would stay in battle; your DS would be expecting your opponent to switch, wait for a switch message from him/her, and behave really oddly when the packet is a move selection from a null Pokémon (!!).
I'm pretty sure you'd need 4 Unown with 1 Hidden Power each on your team to have 4 different Hidden Power types.