At what point is the orchestra told who the Academy Award winner will be?

When everyone else does - when the winners are announced.

I can't find an answer originating directly from the Academy on this, but Time covers the 2014 Oscars and had an article which stated:

• A small team of people (about six people, not including Rosas and Cullinan) split up the ballots so that nobody is counting an entire category, which means nobody knows how the different entries stack up. Those subtotals are added up by Rosas and Cullinan [two accountants]. By Friday evening, the two accountants will know all the winners.

• Though they won’t disclose how many vote are received, there are about 6,000 voting members of the Academy. All of the counting is done by hand. “It’s old-school,” says Cullinan. “It’s as boring as it sounds. You have lots and lots of stacks of little pieces of paper.”

• All of the categories are counted several times, and extra if there’s a tie (which has happened). There has never been a post-awards recount required.

• The Academy provides triplicates of cards listing each movie in every category. Rosas and Cullinan put the winning cards in the envelopes; the losing cards and extras are destroyed.

• Two identical and complete sets of cards are put in two identical briefcases. This year, PwC has introduced a new style of briefcase — seen above — which is the first one to bear the Academy’s logo as well as the accounting firm’s.

• Having rehearsed their blocking on Saturday, Rosas and Cullinan will travel to the show separately, in cars with security details. They carry the briefcases down the red carpet, pausing for interviews, and each take their places on opposite sides of the stage. As presenters come on from either side, they’ll be handed the right cards.

This process is backed up in several other places, including the Journal of Accountancy:

Secrecy is paramount. Team members from PwC meet at an undisclosed location, and each accountant tabulates only a portion of the votes so he or she won’t know the final results. Only Ruiz and Cullinan put everything together in the end to determine who the Oscar winners are, and they commit those results to memory. The winners’ names are not typed into a computer or written down, to avoid potential lost slips of paper or breaches of security.

In the final hours before the Oscars ceremony, Ruiz and Cullinan will quiz each other to make sure they have accurately memorized the winners in each category. They then will look through the preprinted cards for all of the nominees, select those that list each of the victors, and stuff the envelopes. Both will head to the ceremony on Sunday carrying the correct set of envelopes. If one gets hung up in L.A. traffic, the other will also have the results in his or her briefcase. Once at the event, both will be backstage to hand the appropriate envelopes to the celebrity presenters during the live event.

So inferring from what both of these articles say, the orchestra find out when most of the world finds out - when the winner is announced. This means they will likely have rehearsed multiple pieces of music for each winner. As @sanpaco says in his comment above, this is certainly not uncommon for a highly professional musical outfit.