Some champions off the top of my head:
You mention Tryndamere but then say weapons are moot. He does have a huge sword, you know...
He just happens to be buff.
Olaf, on the other hand, was strong enough to battle Lokfar's frost serpent, and survive. Since then, he has survived countless situations that should have killed him (he even survived the Harrowing, and wants to experience it again), and even fought Sejuani's tribe, the Winter's Claw.
Sejuani fought Olaf to a standstill. That says enough right there.
Sion was strong enough to charge through the entire Demacian army just to suffocate the king located in the very back. That strength has been further modified through necromantic means.
Alistar is immensely powerful physically; in his lore (most of which is now considered non-canon due to the the retcon), he single-handedly slaughtered an entire regiment of elite Noxian soldiers before being subdued only by magical means. He even managed to survive the Fleshing.
Malphite is an enormous sentient rock creature, and with an ability labeled Unstoppable Force, it's pretty safe to assume just what kind of strength that entails. His strength ravages the land to an almost irrevocable degree.
Cho'Gath started out small, but he only grew bigger. His strength matches his size; he can easily go toe-to-toe with many of Runeterra's finest warriors; he easily decimates a regiment of soldiers single-handedly in his splash art.
Leona is physically strong, despite her sunlight-related powers. She was born a Rakkor, the Runeterran equivalent of a Spartan, and their warriors only fight when they are outnumbered 10 to 1. Her martial prowess and natural strength is thus on par with Pantheon's, despite heavy armor.
Braum punched through a mountain, and wields a vault door (which was enchanted with True Ice by Lissandra) as a shield. That door isn't light at all by any means; if you look at how he runs in his animations he has a heavy-set bound on one side of his body just to compensate for the size and weight of the shield. Braum is entirely capable of throwing entire icebergs for fun.
Nasus is freaking buff, just saying. He's an immortal ascended being whose strength increases with each slain enemy.
Renekton is strong enough to wield his weapon, forged to scale for his size. He swings it with very little effort.
Both of their ultimates further increase their size and physical strength.
Also, Rek'Sai. She has turned an enormous chunk of the desert into her home. It takes a lot of strength to create tunnels that can accommodate her abnormally large size; her splash art depicts tunnels in solid rock. She's capable of essentially shredding everything in her path with her forearms. She can shred Malphite into tunnel-liner if she wanted to.
tl;dr: A lot of Champions are physically OP. My money's on Ms. Voidling, though.
but it might be Braum, Tryndamere or possibly even Sion. If I remember the lore correctly, these characters have a great reliance on raw physicality.
is the strongest according to lore (Although more people voted Braum).... hmmm, I would have said Braum or Alistar.
punched his way in to a mountain, sure 
shattered a Krag Beast the size of a building with one hit to the head, but I mean it's 
though. He's certainly not League's strongest, but he can make earthquakes through sheer physical prowess for sod's sake. Malphite can do that by just walking around, but I'd imagine he'd give Rammus an A for effort.
, it has to be 
THE BAKER MUST BE APPEASED
is a ascended demigod, so obviously physically strong, enough strength to hold up entire teams.
