The rags-to-riches tale won a leading five prizes, including best picture, at Thursday night's Critics' Choice Awards. "Slumdog" also won honors for director Danny Boyle, writer Simon Beaufoy, star Dev Patel and composer A.R. Rahman.
"It's amazing to see how generous you've been to our film," said Boyle, who called the movie "a love song" to Mumbai.
"You're mad really," he continued backstage. "You're a bit like the Indians are mad about movies. When you find a movie you love, you go for it really."
"I can't presume to speak for him. His voice was as unique as it was original," said Nolan, adding that working with the actor "was one of the greatest experiences any of us ever had or will have."
"His contributions to cinema should be greatly appreciated," Nolan said, "so thanks for this appreciation."
Ledger died of an accidental drug overdose in January 2007.
A humble Penn said the real Harvey Milk would have been his first choice for the starring role.
"He had the charisma that an actor can only aspire to," Penn said.
Co-star Josh Brolin called Penn's turn as the groundbreaking gay politician "the most incredible performance ever."
Milk came into the contest with eight nominations. "The Curious Case of Benjamin Button" also had eight nods, but didn't win a single award.
Kate Winslet was named best supporting actress for "The Reader," while Anne Hathaway and Meryl Streep tied for best actress for "Rachel Getting Married" and "Doubt" respectively.
"Meryl is my idol," Hathaway said backstage. "To win with my idol who I was nominated against is amazing. I'm so thrilled for her and I'm very thrilled for myself, too."
Winslet and Streep weren't on hand to accept their awards, nor was Bruce Springsteen, who won best song for "The Wrestler," from the movie of the same name.
Director Darren Aronofsky accepted on the Boss' behalf.
"I don't know how you put words into the coolest man's mouth," he said, "so I'll just say thank you."
"WALL-E" was the best animated feature and "Tropic Thunder" was best comedy.
"There's a lot of awards out there, and this one, I think, has the most meaning," said writer, director and star Ben Stiller. "I'm not just saying that because this is the only award our movie was nominated for."
Richard Gere received a standing ovation as he accepted the Joel Siegel award, which recognizes an entertainer's humanitarian efforts. The 59-year-old actor is a longtime supporter of Tibet.
"Clearly I'm undeserving of this," Gere said, urging the audience to "channel all that energy to Tibet."
The 14th annual Critics' Choice Awards, presented by the Broadcast Film Critics Association at the Santa Monica Civic Auditorium, honored cinematic excellence in 17 categories. The group, which represents more than 200 TV, radio and online critics from the United States and Canada, founded the Critics' Choice Awards in 1995.