I'm going to Disneyland Tuesday, 14th June. The plan is to stay there until they close at 23:00, and then go straight to Orly to catch an early flight in the morning.
Since I will have a Visite card, I would like to travel from Disneyland to Orly in the evening/night by public transportation (doesn't matter if I have to go back to central Paris first to change) - and not take the shuttle.
Is there a public transport night service which will take me from Disneyland (via Paris if needed) to Orly airport?
The Paris Visite Pass expires at midnight on its last day of validity so I'd recommend you complete your journey by midnight. (All passes, regardless of type, now expire at midnight rather than end of service during the evening.)
The latest route to arrive at Orly Airport before midnight from Disneyland Paris uses the RER A to Nation, transferring to Metro line 6 direction Charles de Gaulle-Etoile until Denfert-Rochereau, transferring to Orlybus towards Orly Airport. Departing Disneyland Paris by the 22:16 RER A train will allow you to reach Orly Airport at 23:37.
If you don't mind buying an extra Ticket t+ for Tram 7 from Villejuif-Louis Aragon Metro you can depart Marne La Vallée at 23:10 to Nation, transfer Metro line 6 direction Charles de Gaulle Etoile until Place d'Italie, transfer to Metro 7 direction Villejuif-Louis Aragon, transfer to Tram 7 direction Porte de l'Essonne (where's where you need a new Ticket t+ as your Paris Visite has expired by this time) until Aeroport d'Orly.