I am not quite sure but I am going to go ahead and try and list the provinces (and individuals) that inhabit the world and how strong they are:
Bandle City: The champs are far and wide and some are pretty mundane (For the sake of this I will list Poppy as Demacian, despite being a yordle), they are technically born with innate magical powers (as stated in Poppy's lore), and some are incredibly smart such as Ziggs and Heimerdinger, who have built weaponry to suit their needs in a fight. The extent of yordle magic is unknown until we get more info, but it seems that Veigar, Lulu, and Gnar are strongest here. Veigar has the ability to warp space and create dark matter. Lulu has the ability to polymorph, increases the size of objects, can use defensive and other disarming spells. Gnar has the ability to become a huge monster and boasts immense strength.
Freljord: Most likely boasts some of the more powerful champs here. Ashe and Sejuani are direct desendants of Avarosa (Ashe) and Serylda (Sejuani) and Lissandra is THE ICE WITCH, they all have some powerful artifact or power that makes them stronger, Ashe has her bow, Sejuani has her True Ice Bola and the Seeker's Armguard (In-lore) and Lissandra has the Ability to take the form of others when she grows old, and the power to manipulate ice. Anivia has been around since the formation of the Freljord, and manipulate ice, she is also a phoenix, thus able the be reborn. Braum is most likely immortal given how many stories there are of him and how he hasn't aged over the course of his adventures, he is very strong, being able to hold a door cursed by Lissandra with little effort, and use it as a weapon, without suffering any consequences. Trundle has Boneshiver (his club), which allows him to manipulate ice similar to Lissandra (though to a lesser extent), he a lot of strength and has an army of trolls under his and Lissandra's command. Nunu has not a lot of power in him, but Willump (his yeti) has lots of magical properties such as his strength, and his ability to suck the heat out in a certain area. Tryndamere is very strong (not as strong Braum however), but he doesn't seem to have any magical power (not yet, but it seems Aatrox has given him some sort of power given his taunt with Trynd) except for becoming completely immune to death for a few seconds, and being able to keep fighting based off his anger. Olaf is also very strong (Getting the picture?), has the ability to call down lightning, and is able to keep fighting even after enduring a lot of damage.
Ionia: Very powerful champions reside here. Syndra has massive control over objects and create sphere that she can use to her will, and he power grows each day, making her more dangerous. The Kinkou Order (Shen, Kennen, and Akali) bring balance in 3 forms, order, light and darkness (Correct me if I'm wrong). Jhin is an artistic killer, the only things he has at his disposal are his gun, Whisper, his imagination, and peoples reaction to his carnage, or his terror. Lee Sin is a incredibly monk and has been taught the Dragon's Rage by the legendary Jesse Perring, a god-like being from the dawn of time. Zed can create shadows that can mimic his actions, and can mark people for death. Karma has the ability to use her abilities for harm and for protection.
Bilgewater: Probably the weakest region on the list and not a lot to talk about, all champs on this list only have weaponry that they can use and that is limited by ammunition , with the exception of Twisted Fate (Who can teleport and use his magic cards) and Illaoi (Who has an idol of the god that she preaches, calling upon it's (he/she?) power). Probably the biggest thing that they can accomplish is defending their city from the Shadow Isles and the Black Mist, but even so, they can barely do it, and most run at first notice, going toe-to-toe with the Shadow Isles is very impressive however.
Mt. Targon: Little is known, but we know one thing, they are powerful. Leona has the ability to use the sun for power and combat, Diana uses the moon. and Pantheon is a fierce warrior who can fight many without effort.
Shadow Isles: has a lot of power and boast what people think are the most powerful champions (I disagree, more on that later). Mordekaiser is the most powerful by a large margin, he controls THE BLACK MIST, has lead an army of warriors during his prime while human, had an impenetrable fortress that is now the capital of Noxus, and can't be killed by any means except for destroying the skeleton of his human form, other wise, he can be revived indefinitely by his liches, the list goes on, but those are his biggest accomplishments and powers. Kalista is (in theory) the embodiment of vengeance, she can make a pact with humans, killing them and becoming part of her, but avenging their betrayal by killing the betrayer. Thresh has the ability to store the souls of his victims, thereby giving them eternal life, but with endless torture to go along with it. Hecarim is very powerful, controling his our onslaught of ghostly horsemen. The list goes on and on, but you guys get the idea.
Piltover and Zaun: They have a broad focus on tech, however a lot of the power is again, far and wide. Vi and Caitlyn are ordinary people who are defenseless without weaponry. Jayce is similar with his Mercury Hammer, he is useless without it. Most don't have a lot of power without their equipment. The notable champs are Viktor, who is a robot with a wide array of weaponry attached to him, his arm on his back, and his Hexcore being the most notable. Warwick, who is very fast, can track creatures in all sorts of shapes and sizes. Ezreal, who has his Ascended gauntlet and he was seemingly born with raw magic in him. Finally, Dr. Mundo and Singed, who are complete juggernauts with lots of strength due to their formulas and potions.
Demacia: Many champions are intresting, to say the least. Garen is INCREDIBLY bulky, and can lift an enormous sword, he has the ability to spin his whole body and sword for a long time without fatigue, and can smite his opponents with some sweet Demacian Justice. Fiora and Vayne are people who just use weaponry and are useless without one. Jarvan IV has a lot of power with his lance, being able to create craters. Shyvana is part dragon. Lux is an very young magic user that can manipulate light. Poppy, oh the little Poppy, has a hammer 2-3 times her size with immense magical powers, she is centuries old (older than Lulu old), her only problem is, she is looking for a hero to fulfill a prophecy of deciding Demacia's fate while unknowingly, she is the hero, when she realizes this, she will have lots of power, maybe finding new powers from her hammer.
Noxus: IMO, a lot stronger than Demacia, many of the champions of Noxus have magical powers or something related to magic. Draven and Darius has their axes that they use with ease. Riven has her rune blade and knows a possible wind technique (remind you of someone?). Swain can turn into a bird and is a strategist. Leblanc can create illusions and can use other forms of magic to deceive or harm people. Vladimir can control the blood in all living things. Talon and Kat are very deadly assassins.
Shurima: Most champs here are bound to magic and /or are Ascended. All Ascendants are immortal, can control something (Nasus controls life and death, Azir controls the memories of Shurima in the form of soldiers, Renekton is a being of hatred and bloodshed, Xerath is magic in its purest form) thus having great influence and power. Sivir is a descendant of Azir, has a boomerang-like weapon (Can someone clarify?) and can block harmful magic. Cassiopeia can turn people to stone and poison them, with no antidote.
The Void: Finally, IMO this is the strongest group. The Void encompasses the space in between all dimensions in the LoL universe, while also controlling an large, unknown number of these dimensions. Kha'Zix is an intelligent, viscous predator who is constantly growing, adapting, evolving, killing beings for more strength, and wishes to kill all creatures that match the Void's strength, and become the most powerful predator. Vel'Koz is similar to Kha'Zix, instead seeking knowledge. Kog'Maw eats things and gains size, not caring for anything else. Malzahar is a prophet that wishes to follow the Void and serve it, having a lot of influence of the minds of other beings. Rek'Sai leads an entire army of her species in Shurima, is fast, and is the size of a house. Finally, Cho'Gath has the ablilty to consume all, no matter the size, and (in the old lore) has the ability to decide the fate of Runeterra due to his power and intelligence.
Individuals will be added later.
and 
go at it in an arm wrestle o.O
would be at the top of that list.
!!!! According to lore he can TURN SOULS TO DUST!!!