The basic dynamic: Odie's expression of unconditional love is overzealous and physically repulsive, and inspires not appreciation but misery. In the Garfield-verse, counting on others for happiness is an unwise proposition, and moments of joy tend to be born from self-reliance and/or self-indulgence. Total obliviousness to others' feelings is a partial explanation of Odie's happiness; ignorance may be bliss, to a degree, but it also gets him put out of the house and branded as an outcast. The other part is simply rushing headlong into what he wants to do. Lest we think Garfield endorses this kamikaze happiness as a successful coping mechanism, note that there is no character as put-upon, loathed or physically abused as Odie. Closer to the truth is that Garfield tells us it's unnatural and stupid to be so optimistic, and in episodes like today's, it is disgusting as well.
Point of consideration: Odie's primary job is foil to Garfield, perpetual optimist to the pessimistic cat. But another aspect of Odie's character is a distilled mirror-version of Jon, specifically Jon's approach to dating; Arbuckle throws himself at women with supreme confidence.
A Note on Cartooning: One of the strip's specialties is suppressing the moment of physical comedy. This is certainly not a hard-and-fast rule, but Davis frequently opts to portray those panels of aftermath, or focus on a character's reaction to off-panel action. Today the scenes of Odie's tongue actually making contact with others are hidden behind sound-effects so large they blot out the action. Add to list of What's Awesome About Garfield: it solves story problems and invents joke structures with techniques specific to the medium, without drawing attention away from the jokes the innovations are supposed to service.
What better panel to advertise the Garfield goodies available via cellular phone, than the image of two angry, miserable characters quietly seething and dripping with saliva? Probably none but the first panel proper, in which Garfield stands motionless and staring into space.