When speaking, how would one say "cannot study"? E.g. 不能学习 or 学习不了 or 无法学习
All of your answers are right. the difference is, on mainland Chinese, 无法学习 is the most formal one, as in scientific reports; 不能学习 is what we say if we are writing dairy/novels. 学习不了 is the most informal one, usually used when talking to friends, etc.

Note I used mainland Chinese, because I don’t know how they say it in HK/TW/Macau.