How did Movie 43 get so many big name stars?

It's actually an anthology, consisting of about a dozen short sketches. It had a budget of $6 million.

Co-director Peter Farelly explains:

...it did take a few years because of the way Charlie Wessler produced it along with John Penotti and myself and from the beginning, they knew the only way to do this was to be able to work with the actor's schedules.

So in other words, when they call someone like Kate Winslet and Hugh Jackman and say, "Hey, would you want to do a short in this compilation film?" They might say, "Yeah, I'd love to but I can't do it for a year and a half" then they'd say, "Okay, we'll wait."

That's how we did it. We had all different crews, all different directors so it was easier to just shut down so we'd go sometimes a year without shooting one and then you'd do like three or four and then you'd wait six months and do a couple more. That's how we did it.

For example, the Hugh Jackman and Kate Winslet sketch was filmed almost 4 years ago.

Charlie Wessler is one of these guys, he's a bit of a Gatsby-like character because you might not have heard his name but everybody in Hollywood knows him.

It's weird. He knows everybody. You'd be sitting in a room and no matter who comes up, he's like "Yeah, I worked with that guy." "What?! What do you mean you used to work with them?" He was a P.A. on "Star Wars" and over the years, he's gotten to know everybody so pretty much everybody in the movie were acquaintances of his that he could just call personally and say "Hey, listen do you want to do this thing? It's only going to take you one day." And they'd be like, "Yeah, sure Charlie, I'll do that."

In short most of them are Wessler's friend and second its due to Wessler's attitude of “Wait for them. Shoot when they want to shoot. Guilt them to death.”

For long read the below mentioned Wikipedia summary:

It took years for Wessler to recruit his actors for the film. He says that he was turned down plenty of times because all the actors were asked to work for scale.

He says. “The truth is, I had a lot of friends who were in this movie. And if they didn’t say yes, this movie wouldn’t have gotten made." In end, most of the actors were willing to take part because the film only required a few days of their time and often allowed them to play a character outside of their wheelhouse.

Hugh Jackman was the first actor Wessler cast. He met the star at a wedding and then called him some time later and pitched him the short. The actor read the script and agreed to be a part of the film. “He called me back I think 24 hours later and said, ‘Yeah I wanna do this,’ which I think is, quite frankly, incredibly ballsy. Because you could be made a fool of, or you could look silly, and there will be people who say, 'That’s crazy; he should never have done it."

After talking to the multiple agents of Kate Winslet, she eventually agreed to take part. The Winslet-Jackman sketch, that was shot shortly after, became the reel to attract other A-list stars.

John Hodgman, who plays opposite Justin Long in one sketch, signed on with no knowledge of the project. Hodgman said, “I got an e-mail from Justin that said, ‘I’m going to be dressing up as Robin again. Do you want to dress up as the Penguin?’ And I said yes. Without even realizing cameras would be involved, or that it would be a movie. Justin is one of the funniest people on earth.”

Richard Gere, said yes — though he wouldn’t be available for more than a year. So Wessler waited him out. He thought the idea of his sketch was too good. Gere eventually called Wessler and told him he was free to shoot, on just a couple of conditions: They had to do it in four days, and they needed to relocate the shoot from Los Angeles to New York.

It didn’t work on everyone. Colin Farrell initially agreed to be in the Butler leprechaun sketch — as Butler’s brother, also a leprechaun — but then he backed out and Gerard Butler did the sketch by himself.

Farrelly says that when he approached George Clooney about playing himself in a sketch (the gag was that Clooney is bad at picking up women), Clooney told him “No fucking way.” There was to be a sketch directed by Bob Odenkirk that starred Anton Yelchin as a necrophiliac who worked at a morgue and had sex with the dead female bodies that was shown at a test screening of the film, but was cut out of the final film. Producer John Penotti said that the sketch will be seen on the DVD and Blu-ray of the film.