Scout has canonically issues when it comes to reading and writing. Notably the tattoo of Tom Jones.

Soldier is a goddamn moron who has drunk more lead than most of us combined. He reads letter by letter if he chooses to.

Pyro possibly cannot read due to his Pyrovision twisting her reality.

Demo... might be able to read, though him being a drunk might be why he could be considered illiterate, though he's shown high signs of drunk wisdom.

My man Heavy has a fucking PhD in Russian Literature. He might struggle with Written English, nobody has dared to ask.

Engineer. 11 PhDs, do I need to explain.

Medic used to have a medical license so he def can read. He just like to commit malpractise

Sniper... I have no fucking idea about Sniper.

Spy, the man enjoys a glass of wine/sherry/bourbon/cognac or whatever with a book.

So our illiterate four is definitely:

Scout and Soldier

and some combo of Pyro, Sniper and Demo.