- Μελετάω translates to read, study, and it's mostly used for academic reasons. Studying and reading for school.
exp. Δεν μπορώ να έρθω στο πάρτι, πρέπει να μελετήσω. - I can't go to the party, I have to read/study.
- Μαθαίνω translates to learn.
exp. Μαθαίνω Ελληνικά - I learn/am learning Greek.
- Διαβάζω translated to read, study, and while it can be used for academic reasons (studying for school), it is more general than μελετάω.
exp. Διαβάζω μια εφημερίδα - I'm reading a newspaper.
I hope this was helpful ^.^