Some Pokemon are weak but there are hilariously weak Pokemon because they are completely useless it's an enigma why they were even included in the game. Nevertheless, they make some interesting stories and discussions.
Electrode
According to Electrode's Pokedex, "It stores electric energy under very high pressure. It often explodes with little or no provocation." So imagine you're this big, shiny, round Pokemon sitting under an apple tree like Newton, an apple fell under your head, and you explode - that's Electrode for you. That also means that one splash from Magikarp can kill this Pokemon. Speaking of explosions, it is also his main attack, which means it will kill itself to defend itself.
Unnamed Pokemon
This second hilariously weak Pokemon has a really hilarious description. Caught by Red in "The Big Battle in the Viridian Forest," there's really no information what this type of Pokemon is. It only says in the information that it is a bug-type Pokemon and that it is supposedly very weak.
Jigglypuff
Jigglypuff is very lightweight that it has almost no kill options as a character. What makes this a hilariously weak Pokemon is that its attack move is to mesmerize its opponents to sleep by singing a soothing lullaby. If the opponent refuses to sleep, this normal/fairy type Pokemon will continue to sing until its lungs run out of air and dies.
Phione
This squid-like mythical water Pokemon came to be by breeding Manaphy. It is not known whether it will evolve into something more. There are some rumors that the only reason Game Freak made this was to have a legendary Pokemon that can breathe. In fact, she is the weaker version of Manaphy which cannot evolve into Manaphy.
Sunkern
This grass-type Pokemon is also known as a seed Pokemon. What makes Sunkern a hilariously weak Pokemon is that its only defense when attacked is to violently shake its leaves as if having some nervous attack. Like Red's unnamed Pokemon, there's not a lot of information about Sunkern except that it suddenly plummeted from the sky. It also doesn't eat anything and its only means of subsistence is morning dew - no wonder it's weak.