What is the legal ruling and what should one do who committed sodomy and sodomy-like acts with his sisters before and after puberty, then repented from that and desires God's forgiveness?

This is a grave sin, but sincere repentance erases sins. If you repent with true repentance, feel remorse, and resolve not to return to it, Allah will forgive your sin. Allah forgives all sins. Allah may purify the believer through calamities. So, if you repent and become righteous, have a good opinion of Allah and hope that He has forgiven you. What afflicts you may not be due to disobedience but rather a trial from Allah. Everything that befalls a believer is good for him, so be patient in adversity and grateful in prosperity.