Here's who I think would be strongest by their races;
Celestials - Bard would be the strongest, as he maintains the nearly-impossible to understand power that allows him to keep everything from being destroyed. Soraka, having abandoned her life as a Celestial, is now weakened and can only beckon the stars to aid.
Humans - This is somewhat debatable, heavily so, so I'll chalk it up to physical and magical strength; the physically strongest human would have to be Braum, being fully and easily capable of holding that frozen door and using it as a shield. The magically strongest human would, in my opinion, be Ryze. Although he'd have competition in the future when Annie Hastur grows up and better hones her sorcery, he's still doubtlessly powerful, through impressive control.
Yordles - Again, chalking it up to physical and magical strength; Poppy is the most physically strong, toting the massive (for her size) Hammer of Orlon into battle, alongside wearing brigandine and plate armor, while the most magically strong, in my opinion, would be Veigar. His magical power is gained through Astral Magics, which would be pretty hard to master. (Note, this is not counting the ancient Yordle Gnar, though if it was, the strongest Yordle's name wouldn't start with a "P".)
Ascendants - Physical strength easily goes to the Butcher of the Sands, as Renekton was most predisposed to physical combat, and thus stationed as Xerath's guard. Magical affinity though would be a little more difficult to pick from, as we've got Nasus, a death-scribe who has some noticeable affinity for fate, Xerath, the Magus Ascendant whose raw magical power was enough to pervert a holy artifact, and Azir, whose Ascended power is enough to raise echoes lost in time of his ancient empire. Although, I'd have to say Xerath is the most magically powerful for the reason stated above.
Voidborn - No point specifying magical prowess, as all Voidborn are in some way magically attuned. At base, Rek'sai would be the strongest of the Voidborn that we know of, although once Cho'gath has spent some time devouring things, he easily overtakes her in power.
Undead - The grasp of Undeath empowers many into wraithborn phantasms and wights that can drain the life of any they encounter. Physically, the strongest of the Undead is Hecarim, who combines the ferocity of man, the power of a warhorse, and the relentlessness of a dark wind. Magically, the strongest of the Undead is another herald of the Shadow Isles, Karthus, whose fascination helped him transcend the boundaries of life and death - and with it, attained fitting semi-spiritual magics.
Other (Humanoid) - We don't have an awful lot of non-human humanoids to judge, but if I had to say, it'd be a tie between Aatrox and Alistar.
Other (Elemental) - This one is, undoubtedly, the Shard of the Monolith, Malphite. He is a mountain, and if anything could be stronger than that, it's time.