Law received a nomination in the Best Actor category for his role in the West End run of Hamlet, which recently transferred to Broadway.
He will go up against former The Wire star Dominic West, who has been recognised for his part in philosophical epic Life Is a Dream.
Mirren will compete against Weisz for the Best Actress trophy for her starring role in Phedre, while the Mummy star received a nod for her turn in A Streetcar Named Desire.
Stewart’s role in Hamlet earned him a nomination for the Best Supporting Actor prize, while he also received a nod in the Theatre Event of the Year category alongside Sir Ian McKellen for their pairing in Waiting for Godot.
Former Spice Girls star Melanie Chisholm has also received a nod for the Best Takeover in a Role for her West End debut in musical Blood Brothers.
The awards will be handed out at a ceremony in London on 14 February (10).