Too Cool! Cartoons, on Cartoon Hangover (YouTube)
Cartoon Hangover; Frederator; Wikipedia

This is an anthology series of eleven cartoon shorts (or ten, if you count the Bee & PuppyCat two-parter as a single episode). It first aired on YouTube between April 2013 and August 2014, but I first heard of it (as far as I recall) in November 2014, after discovering Bee and PuppyCat, which had recently become a series, itself. The anthology is made by Frederator Studios, which is responsible for a number of animated TV series, including other anthologies such as What a Cartoon! and "Oh Yeah! Cartoons," as well as some other animated webseries (including a later anthology, GO! Cartoons). Anyway, I watched all the Too Cool episodes in one afternoon.

Our New Electrical Morals (5:02)
IMDb; Wikia

A guy and a business cat find a baby and try to figure out what to do with it. It's totally crazy and pretty funny. It's based on a web comic I had never heard of.

Rocket Dog (5:34)
IMDb

A crazy rocket dog tries to help his owner get a girlfriend. It's mildly amusing, but basically just weird and kind of disturbing.

Ace Discovery (5:13)
IMDb

Um... a drunken space adventurer and his overeager young sidekick try to find a new fuel source when their spaceship crashes on an alien asteroid. Or something. It's pretty weird and disturbing.

Bee and PuppyCat Part 1 (5:46) & Part 2 (5:10)
IMDb; TV Tropes; Wikia

A young woman named Bee loses her job, then meets a cat (or something) named PuppyCat. And Bee has a friend (potential love interest?) named Deckard. And it turns out that PuppyCat works for some bizarre interdimensional temp service, and Bee ends up tagging along and helping him with his latest bizarre temp job (babysitting a sad, giant space fish). It's awesomely surreal and hilarious.

Doctor Lollipop (5:52)
IMDb; TV Tropes

A dinosaur eats too many fairy tale creatures, and gets a stomach ache, so he goes to see Dr. Lollipop, who is a unicorn. It's reasonably amusing.

Dead End (5:20)
IMDb; TV Tropes

A guy and a girl and a dog who live together all suddenly lose their internet connections. The guy goes to fix the internet, but a ghost pulls his spirit into the internet so she can possess his body. It's weird and reasonably amusing.

Chainsaw Richard (5:38)
IMDb

A boy and a tiny ghost decide to sneak into a movie when they can't afford to buy tickets. But for a boy who's not a ghost, it's a more perilous journey than he bargained for. It's reasonably amusing.

Manly (6:06)
IMDb

Um... a woman named Manly is sent through space to rescue her brother, and um... fight a planet... I dunno, it's just weird.

SpaceBear (5:19)
IMDb

A... space frog or something... and his robot friend... insult a guy who turns out to be an evil space wizard. But then a space bear shows up to bounty hunt the wizard. I guess. It's weird, but funny.

Blackford Manor (6:10)
IMDb

A woman gets a job as a maid at a big creepy mansion, where there are two other servants, but she never sees the master of the manor. So she starts snooping to figure out the mystery. It's all rather creepy and weird, in a gothic sorta way.