What is best way to travel from ORLY to rue cler area of Paris

In the same situation, I'd either take the OrlyVal train or a Taxi from Orly to Antony station, RER B to St.-Michel (short walk required from St.Michel-Notre Dame), RER C to Invalides and then Metro 8 (direction Balard) to Ecole Militaire.

It sounds complicated but it's actually quite straight forward.

Another option would be the Orly bus to Denfert Rochereau, then the Metro 6 line to La Motte-Picquet Grenelle, then change to the Metro 8 line to Ecole Militaire.

If you are going to get a taxi, just take it all the way to your lodging. The fixed fare to Rue Cler area is 30 EUR if you use the official taxi line (and tell the driver you are aware of the fixed rate).

If there is more than one of you then taxi is the only sensible option. It is only 30 Euro. Public transport with Orlyval and then RER and then metro is cumbersome and relatively expensive (about 12.50) so it is only sensible for one person. Be sure you are pickpocket proof if you do that as you are at your most vulnerable lugging all your stuff. No wallets in pockets or backpack.

If you're tired, or have a lot of luggage, just follow the overhead signs to the TAXI stand.
Remember that legitimate taxi drivers never leave their vehicles.
Make certain to hand the driver the complete printed address of where you are staying, including the Postal Code. This way, there won't be any confusion.
Taxis are supposed to accept credit cards, but many will not, so bring cash.
No need to tip unless he helps you with your bags - 1 or 2 EU is fine.

Thank you for all the quick responses.
I think we will follow the idea to take a taxi and not worry about connections with luggage.

Thanks again.

For thirty euros, give yourself a break and let a taxi take you to the door. You can save your energy for seeing Paris.