It is not ours to question the comic strip reality of a cat who has built scale versions of restaurant waiting line placards, nor of a dog who takes commands in written form, nor of that dog's anatomy which is so tortured that it is difficult to recognize at a glance that he is indeed sitting in the third panel. Joke Logic or no, it's a little counterintuitive that a restaurant-protocol gag should take place on top of a table in the house.
That Odie can read is pretty much the crux of the joke, because the associative gap between the meaning of "wait to be seated" and the command for a dog to sit is not very large. There's a second shade of meaning, in which Odie is so dumb he must be ordered both not to sit and to sit. Lord knows what he'd do if given no commands. Squat, maybe? Funnier is how Garfield shuffles through panel two, disinterested, though he is surely the one who made the signs. There are a few levels to these presentational strips in which Odie and Garfield mime a broad joke for us in vaudeville style. We are treated to the joke itself, the acknowledged artificiality of the format, and the self-conscious performances of our silent clowns: Odie with full confidence of the antique material, a happy, catatonic Fatty Arbuckle, and Garfield a weary Buster Keaton, stone-faced with disgust or defeat. The idea of an entertainer so lazy he doesn't care about the audience is a masterstroke. Your comedian is indifferent: laughing is your own job.