He's singing Gangsta's Paradise

"DiDnT yOu KnOw? AlL sAiYaNs CaN dO tHiS"
- Vegeta (I'm a Vegeta fan, it's just he sometimes just makes up bullshit)

It's just an animation exaggeration. I don't think the animators can simply make it look like Goku is screaming in agony, like in the images above, and make it not look a bit off.

Nah. That's a TORIYAMA exaggeration. That's his whole thing.

Those overexaggerations are what made him famous!