I can read, and write, sheet music. But I can’t sight read. Nor do I ever truly read as I am playing.
To learn a bunch of songs quickly, I make simple single-page chord/structure charts. I dissect the structure of the song, write out chords charts for all the different parts, then label each part with a letter: “A, B,” etc., NOT “chorus, bridge,” etc. Then at the end of the page, I write out the order of the parts (e.g. “INTRO, AAB, AAB, C, B, AA, OUTRO”).
If, after that, I am unsure of anything, I keep these notes on my amp or on the floor, or on a music stand if I can put it way to the side. If I am drawing a blank (remembering the song titles is always the hardest part), I refer to them before the song begins, but never during.
I chart like this mainly as a way to quickly commit songs to memory, as opposed to providing myself with something to actually read. Deconstructing, and actually putting pen to paper, really helps my mind to remember things.