Trains from Orly Airport

There is a shuttle train from Orly to the Antony RER station. From there you take the RER train into paris, and then transfer to the metro.

I'd suggest the Paris Museum Card, as that gets you admission into dozens of museums, and allows you to skip the lines at ticket windows.

Versailles is accessible by an RER train from Paris.

The route suggested by #1 costs €9.30. It requires taking the Orlyval to Antony, the RER B to Denfert Rochereau, Metro line 6 to Montparnasse Bienvenue, and Metro line 13 to Duroc.

Cheaper: Take the Orlybus to Denfert Rochereau (€6.00). Buy a single ticket for the Metro (€1.50). Take line 6 to Montparnasse Bienvenue and line 13 to Duroc.

The RER C line goes from Paris to Versailles-Rive Gauche. The C line divides on the west side of Paris so be sure you get on the right train. All trains with the nameplate VICK go to Versailles-Rive Gauche.

Go to www.ratp.fr to download and print a Metro/RER map for central Paris and a RER map that shows service to outlying zones, inlcuding Orly, CDG, and Versailles. Click on the British flag to view the site in English.

The Air France bus coming from Orly used to stop at Duroc on its way to Invalides.

I confirm that the Air France bus (9€) stops on request at Duroc

Sure enough! The Air France bus site lists Duroc as an on-request stop. In that case, ignore the multiple transfer routes I listed in my first post and take the Air France Bus. It will stop at Gare Montparnasse. You'll need to ask to get off at Duroc or it will go straight to Invalides.

and for activities...
not expensive, easy and fun : go to Paris plage, along the Seine (july 20 - August 19)
a walk along the river seeing historical sites from Louvre to the Sully bridge, a rugby play in front of the Hôtel de ville, a drink in a beach chair... and plenty of other relaxing activities

Thank you all for the information. It has been really helpful. I recommend thorntree to every traveller I meet!