Stikbold!'s graphics have a strong Katamari Damacy feel to them. Much like the gameplay, it doesn't try to go for an ultra-realistic visual style. Instead, the game uses blocky characters and set pieces that look more like stylized objects representing the arenas and obstacles than actual representations of those items. This simplified visual style goes a long way to giving off the arcade feel that the game presents. Of course, the fact that the gameplay has the camera pulled really far back so that the entire arena can be seen at once means that any fine details the game developers wanted to try and put into their models would be lost, so not only does the minimalistic visual style give the game a quirky look, but it has a practical reason as well.
Stikbold! continues its quirkiness in the audio department as well. While there is dialogue in the cutscenes, the language isn't quite English, but given how many of the words I understood, I'm pretty sure it wasn't the developers' native Danish either. What gets spoken is a pseudo-English that uses words that are just off, which causes it to become its own unique dialect. While amusing to hear, if you want to know what is actually being said, pay attention to the speech bubbles that pop up.
As for the rest of the game's sounds, the music is delightful and cheery, even when in the depths of Hell (yes, that's right, Hell) and the various sound effects that go off as objects are thrown, people are hit, or the environmental hazards are activated, also sound like they fit in the odd world where dodgeball appears to be everyone's answer to resolving all conflicts.