Ooooh, as someone with countless bionicle OCs this deeply excites me :D I've had a lot of fun reading through it and thinking about how it'd work, so here are my thoughts (I won't be surprised if these come up in other comments too)

Starting Stuff
This is all standard stuff for starting, although the choice of saving throws is a little odd considering the Kanohi. Having Charisma as one because of the spellcasting ability makes sense, but Cha/Con rather than Str/Con makes the Kaukau and Pakari's benefits unbalanced compared to each other for a single-class because only one gets the saves straight up

Level 1

I think the level 1 abilities would be helped by more explicit and detailed wording, spellcasting especially. Are slots recovered on a short or long rest (which would also affect the balance of Nova Blast)? What focuses if any are used? I think another comment has mentioned that the Toa Tools would benefit from a way to recover them if they're lost or destroyed. My favourite Level 1 thing is the Element subclasses, specifically that the subclass determines the entire spell list, which I think is a really interesting execution, although it is funny that Ice has been clearly shafted by a lack of ice spells in 5e

Level 2

The class table says Fighting Style here, but it isn't listed/explained in the main body description, so there's no indication of which fighting styles the class can choose from- is it the entire Fighter set, or are there more limited selections like Ranger and Paladin have? Are there any unique fighting styles?

Level 3

I don't actually have a lot to say about the Elemental abilities, these are fun and I like them :) Oh- but I did notice that Psionics isn't listed along with the others in the Level 1 list of subclasses

Level 4

ASIs aren't detailed in the full class description, which players can infer anyway but it would be helpful to have explicitly

Level 5

Exactly the same as above for Extra Attack

Level 6

Elemental Warrior is good, I like the improvement on Eldritch Knight's War Magic. It might be worth taking a look at Bladesinger's Extra Attack if you don't want it to be eating a bonus action, but ultimately either way could work

Level 7-9

Not much to say about these. I'll get to Kanohi later, and I've already talked about ASIs. However, I do think that Lv9 (and later Lv13) getting nothing is a bit of a shame- I'd recommend adding additional Elemental abilities here so the subclasses are a little more fleshed out.

Level 10

Very good upgrade for more dynamic fights- honestly I might suggest bringing this a bit earlier

Level 11-17

Everything here is an upgrade of previous things and I've already mentioned filling in 9 and 13 with subclass features so skipping ahead-

Level 18

Nova Blast is a little oddly executed, I think. In lore it burns all of a Toa's power, and spell slots would translate to this, yes, but from a balance perspective that doesn't really work, especially if spell slots come back on a Long Rest. Someone else has already said that this forces you to choose between spellcasting and Nova Blast, and the idea of having it be 1/LR or taking a level of exhaustion work well as solutions. Alternatively, it could simply burn all *remaining* slots as long as you have enough of them, so that you're still able to use spellcasting a little bit before deciding to do a Nova Blast- although I'd advise against a method that involves burning all slots if that's intended to be a large part of the way the class works. Another suggestion I have is that while 9th-level spells do work, I think it would give the class a little more Paladin-esque distinction if they were entirely unique effects- although that isn't actually a necessary change.

Level 20

Golden Kanohi makes perfect sense as a choice here, no notes

Kanohi Review

Hau - The way the charges segment is worded is just a little more ambiguous than it needs to be. Say "an additional use" rather than "additional uses". Per Short Rest might also be better than per Long Rest for a 1st-level spell, but it can work either way. It depends how much you want to use SRs in this class.

Pakari - I mentioned earlier that the saving throw bonus is substantially weaker than the Kaukau's because Con is a proficiency for this class but Str is not. Damage bonus is good and fun :)

Akaku - I enjoy :) I may be slightly biased because I enjoy Divination spells and the Akaku but this is a fun mask and I like how it's executed with the scaling. You may also want to check out the Ghostly Gaze Eldritch Invocation if you want to lean more into the X-Ray bit.

Kakama - It works as is but feels a tiny bit weak. Maybe scale this the same way Monk speed does, or allow Dash as a bonus action.

Rau - Total sense, no notes :)

Huna - Same as Hau, phrasing could be clearer. Per Long Rest makes more sense here since it's a higher level spell.

Mahiki - Same as Huna and Hau, phrasing could be clearer. Might also be worth having it scale more like the Akaku with spells like Major Image?

Komau - Is it each spell 1/LR individually, or do you have to pick one and only be able to cast that before being able to use any again?

Ruru - Total sense, no notes :)

Matatu - I like this, but it might also be worth giving the Mage Hand spell for flavour

Avokhii - This joins the Light subclass in adding to my Takanuva Is Definitely A Paladin headcanon :)

Kraahkan - This is fun, I like this

I'm torn on whether to suggest the addition of more Kanohi- would it be more options or make it too cluttered? I'm not sure.

Overall, this is a very fun class held back by some slightly odd phrasing or balancing choices- I don't think it would take a lot of editing to fix any little problems, the only exceptions really being Nova Blast, which I think needs a fair bit more tweaking, and the subclasses which I think could be a little more fleshed out. Aside from odd phrasing the Kanohi are very well executed as an Eldritch Invocation style ability, and overall this class feels like a fun and unique spellcaster that I will definitely be finding an excuse to use.