The title card for The Sludge Monster appears in the episode The Lssagne Zone in which Garfield finds himself trapped in the TV hopping from channel to channel in various shows.
In the U.S. Acres episode, Fortune Kooky, Roy looks at a calendar that displays a picture of Garfield wearing a party hat and the words 'happy 10th birthday Garf'. Garfield was indeed celebrating 10 years since his first appearance in a comic strip at the time the episode aired.
The Sludge Monster originated in the Garfield comics in 1980. Though unseen, it was first referenced in the April 24th strip as a drive-in movie, "The Sludge Monster Meets Vermin Man", which Jon and Garfield had seen eight times. A week-long story-line ran from June 30th to July 5th, 1980, in which Garfield watches a Sludge Monster movie on TV, then hunts for him around the house.