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Translations: Gintama 515 (2)
Guts is without any doubt a human. As Franckie said above, he developed the strength after years of years of battling. I will quote an example of real life:
I used to play Squash. The racket I had previously weighed 110 grams. It broke and the one I bought weighed around 150 grams. It felt so heavy when I started to use it. But after few weeks I didn't realize any difference.
My point is, back when Guts was young we saw him going for the bigger and heavier swords, he developed physically to handle the extra size and weight. Swinging that sword and battling over the years added to his overall physical prowess as well. More than anything its adrenalin and his will to survive that makes him super strong. He has always looked and felt like a human to me. It will be more fitting for the story as well, seeing God Hand(s) beaten by a mere human, assuming. His strength is already nearing to that of an apostle like Zodd or others.
Of course he's a human