From Answers.com:

Plot Summary

Act I: the Initial Poker Game

The Odd Couple opens on a hot summer night in the large, twelfth-floor apartment of New York City sportswriter Oscar Madison. A few months earlier, before Oscar’s wife left him, the apartment had reflected the modest luxury of its Riverside Drive neighborhood on the Upper East Side of Manhattan. But the apartment is now a mess because Oscar is very sloppy and his weekly poker game is in progress. Dirty dishes, empty bottles, half-filled glasses, ashtrays, and other messes created by the poker game have been added to the discarded clothes, old newspapers, magazines, mail, and disarrayed furniture that are part of Oscar’s everyday sloppiness.

As the curtain rises on this smoke-filled room we see Murray, Roy, Speed, and Vinnie around the poker table. They are concerned about the unusual lateness of one of their regular poker players, Felix Ungar. Oscar enters from the kitchen with food for his buddies, the phone rings. It’s Oscar’s wife complaining about his overdue alimony payments. Two more phone calls, one from Murray’s wife and another to Felix’s wife, Frances, inform everyone that Felix is missing because earlier in the day his wife declared an end to their twelve-year marriage. The poker players worry that the sensitive Felix might be contemplating suicide, and when he finally arrives at Oscar’s apartment they try to pretend that everything is normal while simultaneously interpreting everything Felix does as a preamble to suicide. Felix admits that earlier in the day he swallowed a whole bottle of pills but then vomited them up. After heartfelt expressions of concern, Murray, Roy, Speed, and Vinnie go home, and Oscar tries to console Felix, massaging his neck and back, pouring him a drink. When Felix hums and hops from leg to leg, bellowing like a moose to clear his ears, we get an indication of the eccentricity that might have led his wife to expel him. Felix confesses that he was unbearably obsessive about such things as petty finances, cleaning house, and cooking. Oscar sympathizes by describing the traits that led his wife to leave him. He invites Felix to move in with him, admitting that he doesn’t like living alone. Felix agrees, imagining all the ways he can help Oscar — from fixing things to cooking and cleaning. During this discussion, Felix’s wife calls but only to find out when Felix is coming back for his clothes (she wants to have the bedroom repainted). Felix declares his acceptance of the failed marriage and starts to clean up Oscar’s apartment, responding to Oscar’s goodnight by calling Oscar by his wife’s name, Frances.

Act II, Scene 1: the Second Poker Game

Two weeks later, about eleven at night, another poker game is in session, but this time the apartment is immaculately clean. Felix appears from the kitchen with carefully prepared food and reminds all the players to use their coasters to preserve the carefully applied finish on the table. Some of the players, like Vinnie, are quite pleased with the new atmosphere. Others, like Oscar and Speed, are aggravated by the excessive concern for tidiness. The game breaks up prematurely and Murray is the last to leave, commenting on how happy he thinks Oscar and Felix must be living the bachelor life. But in the argument that ensues following Murray’s departure, Oscar makes it clear that he is very unhappy living with the excessively tidy Felix. He asserts that Felix is obsessive about controlling things, including his own emotions, and ought to loosen up, relax, and have more fun. But when Felix tries to express his anger by throwing a cup against the door, he hurts his shoulder. Oscar’s plan for loosening up and having more fun is to invite to dinner two attractive sisters from the upstairs apartment. Gwendolyn and Cecily Pigeon are British (they say “solicitor” instead of “lawyer”). Oscar met them on the elevator a week earlier, and he is eager to get to know them better. Felix, however, feels a loyalty to his estranged wife that makes “dating” seem wrong to him. Following an argument, Felix finally relents and agrees to help entertain the Pigeon sisters — provided he can cook the dinner. He calls his wife to ask for her recipe for London broil.

Act II, Scene 2: an Evening with the Pigeon Sisters

A few days later, about eight at night, the dining room table is set elegantly for four. Felix is in the kitchen when Oscar enters cheerily. But Felix is angry because Oscar had told him he would be home at seven and that the sisters would arrive by seven-thirty. The dinner, planned for eight o’clock, is nearly ruined. Gwendolyn and Cecily arrive and they all sit, but Felix does not join the conversation until he comments, quite inappropriately, on the weather. When Oscar goes into the kitchen to fix drinks, Felix becomes the center of attention for the Pigeon sisters and tells them how much he misses his wife and children. This is not what Oscar had in mind for trying to romance the women, but Gwendoyn and Cecily find Felix “sensitive.” When Oscar comes from the kitchen with their drinks all three are crying. Felix rushes into the kitchen to inspect his burned London broil and when he dejectedly returns, Gwendolyn and Cecily suggest that they all go upstairs to their apartment for dinner. The sisters leave to prepare but Felix tells Oscar he won’t go because it would mean being unfaithful to his wife and children. Oscar goes upstairs alone, angrily accusing Felix of being unwilling to change, suggesting sarcastically that if he wants to commit suicide the apartment is indeed twelve floors from the pavement.

Act III: the Last Poker Game

The next evening, about seven-thirty, the apartment is set up for yet another poker game. Felix is vacuuming when Oscar comes in, still angry about the previous evening’s failure with the Pigeon sisters. They argue and Oscar begins to sabatoge Felix’s efforts at cleaning, finally throwing a plate of linguini against the kitchen wall. Oscar gets Felix’s suitcase and demands that Felix move out. Felix leaves just as the other poker players arrive. His friends are worried about him but have started to play poker nonetheless. The doorbell rings and Gwendolyn, Cecily, and Felix appear. They have come for Felix’s things because he is going to move in with the Pigeon sisters for a few days until he gets settled. Oscar and Felix shake hands just as Oscar’s wife calls on the phone. Oscar sent her money to pay all his alimony, and he expresses a desire to talk with her again. As he is going out the door, Felix promises to come back for the next week’s poker game. The poker game begins and Oscar admonishes the players to be careful of their cigarette butts.