When Mike Nichols directed THE ODD COUPLE on Broadway (Art Carney played Felix; Walter Matthau) the cast laughed all the way through the first reading. Nichols then said, "Okay, from now on read it like we're doing HAMLET."
The point is that for the characters -- from their point of view -- it's life and death. It's extremely serious.
Think about THE ODD COUPLE. Felix is suicidal. He's lost his family -- his beloved wife and kids. Oscar hasn't paid his child support and is facing jail. He's a deadbeat dad and compulsive gambler. These guys are stuck together and on the verge of killing each other. Go back and watch it with this in mind. Then see Simon's great comic choices.
If the actors are mugging it or winking their way through then the audience knows they are in on it. And it's not funny. The actor needs to experience the pain and suffering and treat it as a matter of laugh and death. Now that's comedy!