On animal crossing wild world when does the weird character come?

If by the dog you mean K.K. Slider, he comes on a Saturday night between 8.30 and 10.30/11 pm. To find out about what songs you can get to play on your radio check out the website below. It has a list of items, bugs, fish, songs, fossils, characters as well as info that may help you work your way through the game. http://www.gamefaqs.com/portable/ds/game/920786.htmlEnjoy!