are the only true Hybrids in the game, and as someone said earlier usually they slide into one of the categories getting gunblade and then AD or AP.
Jax genuinue hybrid works with every item though. Ionians, Triforce, Gunblade, Rageblade, Steraks, GA with 10% CDR from Runes gets you plenty of Raw AD AP and AS with 40% CDR
Akali kinda hybrid builds gunblade then AP, but thats more the failure of her class. She is supposed to be an assassin, and generally AP is better than AD for burst.
Kayle mostly hybrid, she can build On-Hit, hybrid, or AP all with her primary focus with AS. Ionians/Zerks/Sorcs, Nashers, Rageblade, Rylais, Hurricane, Void Staff.
Current hybrid itemization favors drawn out fights, so as an assassin it just doesnt favor Akali.