Pianists can play complex songs with lots of notes and finger positions thanks to muscle memory. Yet, they only acquire such memory because they practice a lot with the sheet music (or Synthesia for newbie piano players like me :D) until being able to play perfectly without it.
What I'm trying to say is that memorizing Invoker's hotkeys is all about practicing. Go play random pubs, use -invokelist every game and try casting things until you get that muscle memory. You'll mess up, you'll forget to use some skills (I played many games when trying to learn Invoker where I went QE build and completely forgot Ice Wall lol), but eventually you'll be able to effectively cast what you need for any situation without stopping and thinking what keys you need to press to land that meteor, for example.
I also advocate practicing with real people (even low level pubs, srlsy) instead of going single player, as you need to learn which situations demands an specific spell and you won't find all of them by trying to cast stuff on creeps.
P.S.: About the macro stuff, I also find them cheating, like, using turbo controllers in certain console games.