As he hangs up his coat in the closet, he starts to sing 'Cocktails for Two' and Oscar slams the door on him. The joke is paid off at the very end of the show, when Felix admits Oscar was dead on about him, except that he, Felix, is a better singer. I Gotta Be Me-During the role reversal scene, Oscar talls Murray and Miriam to swirl the wine in their mouths until it tastes like furniture polish, and while they do so, he begins singing 'Cocktails for Two'. Langley keeps tapping and won't stop, even as Felix keeps trying to push her aside. Maybe someone else knows what song it is. I don't recognize the song, and the tapping drowns out Al Molinaro's singing. Langley is introduced at the party, she does a tap dance to a song Murray plucks on the ukulele and sings. Oscar's Birthday-I must confess my ignorance this time. Oscar's mother says, 'Maybe it's the radio,' and Blanche responds, 'If it is, it's an old one.' Oscar, looking stricken, says, 'And burglars don't sing.' He disappears down the hallway, and Felix's singing is interrupted by the sound of him being choked. Later, when Oscar, Blanche and Oscar's mother come home from the restaurant, they hear Felix singing 'Peg O' My Heart' in the bathroom to the plant. Of course, Felix begins singing the song. The Odd Couples-When Felix asks Oscar to take care of his fern, he suggests singing to it, mentioning that it likes 'Peg O' My Heart'. Inserts of the animals' bemused reactions are edited in. I'm Dying of Unger-When Felix first plans to go out to the store, he opens the cabin door and begins to sing 'Indian Love Call' to the birds and animals. The Odd Monks- In telling about his day, after Felix mentions cloud-watching, he starts to sing 'Look For the Silver Lining' and everyone disappears to play Sugar Cube Craps. The Murray Who Came To Dinner-Oscar and Felix both sing a few bars of 'I Got The Sun in the Morning' in Oscar's room, and then Oscar reprises it when he walks in on Murray's drawing lesson. Speak for Yourself-Several instances of 'Just One More Chance' are changed to an up-tempo tune I don't recognize. I found this list someone put together of the edits, by season and episode:

The odd couple season 4 episode 5