Law, the star of the films Sherlock Holmes and The Talented Mr Ripley, and Stoppard, whose career in theatre and cinema has spanned half a century, took to the boards of the Good Chance Theatre, which was set up by British volunteers last year.
About 200 camp residents watched the performance, which involved British actors, comedians and singers, including Tom Odell and Toby Jones.
The event was organised by Letters Live, which organises readings of letters from historical figures, and featured writings by refugees in the camp.
Law helped organise a petition to UK Prime Minister David Cameron last week, calling on him to allow children in the Jungle with relatives in Britain to be reunited with their families while their asylum cases are heard.
It also also urges him to press France to put off plans to raze the southern part of the Jungle by Tuesday.
There are 440 children living in the section, 291 of them unaccompanied, according to charity Help Refugees.
The official responsible for the eviction ultimatum, Fabienne Buccio, on Sunday declared that she would do all she could to avoid the use of force on Tuesday and would work with NGOs, several of whom oppose the move, to clear the area peacefully.
Eight people, six migrants and two solidarity demonstrators, were to be sentenced by a court in nearby Boulogne-sur-mer on Monday in relation to the boarding of the ferry Spirit of Britain during a demonstration on 23 January.
Around 2,000 people took part in a demonstration calling on Britain to accept asylum-seekers on the day.
About 150 of them broke through a barrier around the port and boarded the ferry.
Police removed them after three hours and arrested 24 migrants and 11 members of the No Border Network, an organisation that campaigns against migration controls and has been accused by the French government of inciting migrants to violence.