No accent with του because it's not ambiguous. If the subject was η γυναίκα then an accent helps to distinguish whether it refers to "his wife" (no accent) or "the women [reads] to him" (accent). The ideal situation for written modern Gk is clear, but what I'm not sure about yet is whether there is an intonation difference when someone is speaking.
Think of it as the following in the English sentence 'I give a present to you': the verb takes two objects, a direct one (a present) and an indirect one that is introduced with a preposition (to you). This is how the example above works too: She reads him a newspaper = she reads a newspaper to him = Αυτή διαβάζει μία εφημερίδα σε αυτόν = Αυτή του διαβάζει μία εφημερίδα.
This direct - indirect distinction explains why the weak form of the object pronoun that goes before the verb in Greek is either in the genitive case or in the accusative: βλέπω εσένα (σε βλέπω, direct), μιλάω σε εσένα (σου μιλάω, indirect).
There are differences between how Greek and English verbs work, so one that takes a direct object in one language may take an indirect in the other. For example: Ι look at you = Κοιτάω εσένα = σε κοιτάω - the Greek verb is followed by a direct object.
Αυτή του διαβάζει μια εφημερίδα. Directly translated: She him read a newspaper. English: She reads him a newspaper/A newspaper she reads him/She reads a newspaper for/to him.
Αυτή τού διαβάζει μία εφημερίδα. She (is) his read a newspaper. Better: She is his reading a newspaper. (Αυτη τού διαβάζεται μία εφημερίδα).