Family Guy seems to be fond of this type of humor:
Peter and the Bullfrog
Peter and the forklift [Graphic]
Then there’s a newer one that hasn’t made it to YT yet of Peter trying to open a can of Spinach.
I don’t know what it is about this particular brand of humor but it cracks me up every time.
I would call it “macabre humor”, “gallows humor”, or “gross-out jokes”
Family Guy draaaaaags out jokes, is that what you’re referring to? Or are you talking specifically about the jokes you posted (which could be considered ‘gross’ or ‘awkward’ )?
Would this fit into what you’re asking about?
“Milking”
Wait a minute. Which aspect of the joke are you referring to? The dead body, or Peter’s unsuccessful attempts to get rid of it? If the latter, how about “frustration”?
Nearest I can think of is a Shaggy Dog story where it isn’t the punch line that’s the joke, but rather the process of telling an increasingly convoluted or lengthy joke. The (in)famous “Aristocrats” is probably the same thing.
There’s a theory that when you extend a joke it gets funnier and funnier until it stops being funny but if you keep going beyond that, eventually it gets funny again. Mike Meyers also does a lot of jokes like this in the Austin Powers movies.
ETA: I really felt bad for that whale.
I’m not talking about the gross out factor, I’m referring to making several attempts to do something and failing every time.
Ludicrous? Over-the-top? If it is the repetition beyond humor that eventually—through additional repetitions—becomes funny again… Maybe “Double-Psych.”
Is it called an overly long gag, on TV Tropes page, where it goes to the point where the sheer length becomes the gag. I think the Simpsons Rake scene with Sideshow Bob does it best.
Yeah, at some point the length they take the joke definitely becomes the joke itself. There seems to be a particular amount of timing about this.
With the bullfrog, they could have ended the joke with Peter’s initial reaction. “Hey Chris I got you a bullfrog ohhhh it died.” 
When he’s repeatedly trying to throw it out the window without actually touching it, I think it becomes funny both because of the length and people relating to similar awkward/macabe situations; I can remember trying to gingerly remove a disgusting squirrel corpse from my front yard (I think I also had a shoebox, coincedentally) and the stupid corpse just Wouldn’t.Go.In.The.Box. At some point I had looked up, and realized a kid on a bicycle had been watching me the whole time, probably with great amusement.
This is it. Family Guy would be far better if they ever understood the point where the joke just stops being funny (not that this particular one was all that funny to begin with, but they have had some brilliant jokes that were killed by McFarland’s penchant for not knowing when to stop).
I’d call it a combination of “locus ad absurdum” and “locus ad nauseum.”
I’d also call it “When the hell is this gonna stop already?”
Frankly, I’m not a big fan of Family Guy. However, I thought those clips were hilarious, as well as a little uncomfortable. A big part of Peter’s character is that he’s just too stupid to know when to stop. He compounds his idiocy with pure bull-headedness. It’s pure satire.
What to call it? I think Overly-Long Gag fits nicely, while the gross-out factor contributes by making it seem even more wrong.
My favorite example is the vomit scene in Team America: World Police. I’m cracking up just thinking about it.