While arguing over whether to eat leftover pizza from the garbage bin – it was only just thrown out and is still in the box – Rory calls Lorelai “Oscar”, and she counters by calling Rory “Felix”.
This is in reference to Oscar Madison and Felix Ungar, the main characters from The Odd Couple, originally a 1965 Broadway play written by Neil Simon. In the story, the pair are friends sharing an apartment, with the slovenly Oscar and neat-freak Felix constantly clashing.
The Odd Couple was made into a comedy film in 1968, directed by Gene Saks, and with Walter Matthau and Jack Lemmon starring as Oscar and Felix respectively. Given rave reviews by critics, it was the #4 film of 1968.
It was then made into a television sitcom with Jack Klugman and Tony Randall as Oscar and Felix, originally airing from 1970 to 1975, but still on American television in reruns. This may be the version of The Odd Couple that Lorelai and Rory is most familiar with.
It seems to be an old joke between Lorelai and Rory to see themselves as “the odd couple” – mismatched housemates who nevertheless are very fond of each other.
(Note that Lorelai cleaning out the refrigerator is a call back to the contest she and Rory had at the start of the episode to see who had to clean out the fridge – apparently Lorelai lost).