Challenge: Provide canon evidence that Klingons are, on average, stronger than humans. Either by way of demonstration or a statement to that effect.
This is commonly accepted to be a fact among fans. Taking a look at references in Memory Alpha:
Klingons were larger and physically stronger than most species, they possessed a much lower tolerance to the cold. (VOY
: "Change of Heart
Both of those references support the "tolerance to the cold" aspect, but make no mention of the strength part.
Compare this to Vulcans, who are explicitly stated to be three times stronger than humans (DS9: "Take Me Out to the Holosuite") are are shown performing feats of strength (such as when Spock punches in a computer terminal with his bare hands).
The closest I have been able to find is in Voyager, where a Vulcan proposes that a Vulcan would be better able to withstand Klingon mating practices than other humanoid species.
However, he doesn't explicitly say he is better than a human in this regard, and we have examples of human-Klingon bonds.
Breaking things down further:
The Original Series Klingons are just humans with bronzer. Not even the implication that they are, as a species, stronger than humans. More ruthless and warlike, sure, but not necessarily stronger.
In The Next Generation, they take on a more menacing appearance, despite being "friends." It is in TNG they this reputation for strength comes from, though never actually supported. We learn about their multiple redundant organs, penchant for live martial sparring exercises, and tendency to engage in a sort of "blood lust."
But, as you note, just about any trained human is able to hold their own against similarly trained Klingons.
I think the advantage that Klingons have over humans is primarily cultural. They enjoy fighting and don't really care who they are fighting with and they go to extreme lengths when fighting. Think Japanese in WWII. The Japanese weren't inherently stronger, they just had a different cultural mindset.
However, Klingons do have biological advantages. The are bigger on average than humans and the aforementioned redundant organs. This allows them to survive injuries that would be lethal to humans. They also clearly have superior endurance and stamina. Both of those combined could give the illusion of superior strength, especially on the long term.