I normally make full character kits on request, but I'm not building five of them for you, so here is the general idea instead.
Pig
Passive - Pig gains extra gold from all sources, scaling slightly with the amount he already has.
Q - Pig charges forward, becoming immune to slows and immobilzations while he moves while damaging enemies he comes into contact with. When he hits an enemy champion, it damages and stuns them while forcing Pig to stop.
W - Pig bites into an enemy, stealing a % of their HP in physical damage and slowing them.
E - Passively, Pig regenerates a % of his HP while out of combat with champions/tower/epic monsters. Actively, Pig gains a % of attack speed equal to his current missing HP for a few seconds (% does not update over the ability time).
R - Pig gains a massive amount of movement speed and AD for a brief period.
Turtle
Passive - Turtle takes the greater of a % and a flat value less damage from all effects.
Q - Turtle enters his shell, massively boosting his armor and magic resist, reducing his vision radius (think Quinn blind), and changing his movement speed to an accelerate system (starts at 0 and builds up as he continues in a similar direction) up to around double his movement speed. Can be reactivated to cancel at any point after 1 second.
W - If Turtle is in his shell, activating this ability changes his direction with minimal loss in speed and changes the type of movement to a dash until he impacts something or reactivates this ability. If the hit entity is an enemy, he leaps out of his shell and tackles it, preventing the target from moving until Turtle moves or uses another ability. If he is out of the shell, it grants him a slight attack range buff.
E - Turtle charges, increasing his base AD and movement speed by a middling amount towards enemy champions. If he attacks one during the duration, he loses the buff by they lose armor equal to the AD bonus and are slowed.
R - Passively, Turtle gains increased armor and magic resist. Actively, Turtle reduces all incoming CC and damage by a large % while absorbing all projectiles that pass over him.
Lobster (Crabgot dude... It counts)
Passive - Lobster has a larger arm, that deals bonus damage on hit and has a longer range, but it has a minimum range.
Q - Lobster grips an enemy champion in his pincer, stunning them briefly and applying damage. This stops him from using his passive for the duration. Enemies are dragged behind like with Skarner.
W - Lobster lunges forward, gaining increased attack speed for a moment.
E - Lobster passively gains an shield which blocks damage that would be dealt to him which would drop him below 50% HP. While the shield is active, he gains increased armor.
R - Lobster, taking after the pistol shrimp, shoots a projectile from his larger claw (minimum range, again), which deals damage in an AoE and sucks enemies towards the center.
Fish
Passive- Fish has a limited amount of 'Air', which lasts for a time that scales with Fish's level and HP. This is instantly refreshed while in the river or fountain, but is slowly refreshed while not moving. Additionally, Fish gains a massive increase in movement speed on the river which scales with level and AP.
Q - Fish leaps into the air, draining a little bit of Air, and crashes onto the ground a distance away. Enemies hit are knocked away slightly and take damage scaling with AP and HP. If Fish is in the river, he instead dives under (becoming invulnerable and untargetable for the duration) and comes up at the target location for an extended knockup.
W - Fish flops around, losing a bit of movement speed while decreasing damage taken from non-AoE sources by a large amount. (I would put dodge here, but Riot seems adamant about keeping it out.)
E - Fish gains movement speed for a brief moment, which also speeds up the cast time of all of his abilities and increases the % damage reduction on his W.
R - Fish springs towards an enemy champion, dealing AP scaling damage and resetting the cooldown of his other abilities.
Penguin
Passive - Penguin leaves behind a trail as he walks which lasts for a rather long time. If an ally walks over it, they gain increased movement speed, though that bonus is doubled for Penguin.
Q - Penguin shoots out a projectile, damaging and slowing the first target hit. The projectile path leaves a trail of his passive.
W - Penguin doubles the bonus from his passive (again) and moves along it. If he moves off the path, he is slowed momentarily. If he attacks an enemy champion with this ability active, it deals bonus damage based on his bonus movement speed.
E - So long as Penguin is moving along his passive path, he can dash a short distance to an enemy and deal AD scaling damage to them.
R - WE CAN FLY!: Penguin leaps into the air, granting him a second to target an area from untargetability. He lands there, dealing damage and leaving a large circle of his passive trail.