Is it permissible for a brother to intervene in the religious upbringing of his younger sister, despite the opposition of the parents and their accusation of him being overly strict, and is his intervention considered an overstep against those who are older and have more right to her upbringing?

If your parents have not taken responsibility for guiding and raising your sister, then there is no harm in you doing so. In fact, it is a religiously required act, falling under the rubric of offering advice to every Muslim. Your guidance for her should involve directing her to her religious and worldly interests, teaching her what she is ignorant of concerning her religion, warding off harms and bringing benefits to her, and enjoining good and forbidding evil. This should be done with sincerity, gentleness, and compassion, and by being a good role model for her. The fact that you are the youngest of your siblings does not prevent you from fulfilling this role, especially if no one else is doing so. It is also appropriate to gently remind your parents that their daughter is a trust with them, and that it is their duty to provide her with a good upbringing.