Which Characters Bios are not canon?

Malphite, Kayle, Morgana, Nocturne, Fiddlesticks and Cho'Gath have completely non canon lores as everything about them is linked to the Institute of War. It's unknown what will be carried over, but in some cases there's sod all to carry over cough cough Fiddlesticks cough Nocturne cough cough.

Lee Sin, Nautilus, Orianna, Brand, Alistar, Janna and Shaco have large sections of their lore that aren't canon, but elements that are essentially the foundations for what will come (Lee being a magic user who then repents by becoming a monk, Nautilus being left to die, Brand inhabiting Keghan Rhode, etc). Not very trustworthy regardless though.

Zed, Galio, Vi, Kennen, Akali, Zilean, Wukong and Maokai have odd lore that's canon in some ways and isn't in others, but it all still fits within the new canon regardless. It's odd. I'll briefly describe why here:

• Zed, Kennen and Akali's lores will have changes because of changes brought by Shen's new lore and how he operates. His new bio directly affects how their lore now works.
• Galio's lore was intrinsically tied to Poppy's, and now that Poppy's has changed the circumstances around Galio's have also changed.
• Vi's lore is muddied by details brought to the table by Ekko, so it's not easy to say what's exactly true here. It could all be, Ekko just makes things a tad muddled.
• Wukong's lore was weirded out when Master Yi's lore was updated. For all intents and purposes Master Yi's lore can be considered the canon version of how Wukong and Yi met, but details about other parts of Wukongs lore are up in the air anyway.
• Zilean's lore's been left in the dust but Vel'Koz reaffirms that it's still a thing. It's kinda odd because where as the champs listed above bring changes to other champion's bios, Vel'Koz reaffirms Zilean's by reassuring us that Urtistan is still canon, as is Zilean's clock tower. What else is canon is anyone's guess.
• Maokai's current bio seems to have been built using an earlier version of the Shadow Isles backstory that wasn't fully nailed down at the time, and changed somewhat over the course of a few months. The current Shadow Isles backstory was almost certainly nailed down by Kalista's release, so Mao's is a bit odd.

In those special cases there details about the champ's bios can be extrapolated from new lore, especially in the case of Maokai; just change some phrasing and it works out perfectly.

That's all I can think of at the moment.

Only the ones that are directly connected to the Institute of War are not considered canon actually. The rest can be loosely seen as canon/give an idea of what the champions are once their Lore is redone. The following aren't canon:

i think are not canon, unless they got a lore update they went over my head XD

It depends. Some older champ's lore can still be considered canon so long as you take out whatever ties to the IoW and summoners and it still makes a story.

Arguably none of them are canon, since any of them could be retconned at any moment as Riot's mercurial vision of what the game's lore is supposed to be shifts. The purpose of having a 'canon' is to have a shared body of lore that everyone can agree on as the factual basis for a setting. League has nothing like that, it's one big contradictory mess.