This page explains in detail the interactions between the Haiyore! Nyaruko-san series and the Mario series.
Haiyore! Nyaruko-san episode Blue Coral Reef[]
May 21, 2012
In the seventh episode of the anime, when Mahiro's mother, Yoriko, allows Nyaruko to go on a date with her son, Nyaruko jumps for joy in a pose greatly resembling Mario's jumping pose, and the background momentarly changes to a Super Mario Bros. setting.
Haiyore! Nyaruko-san episode Lost Girl from the Stars[]
May 21, 2012
The eleventh episode of the anime opens with Nyaruko, Cthuko and Hastur playing a videogame that's implied to be a Mario Kart game, since the characters' dialogue mentions drifting, throwing shells and bananas. Since they're using Nintendo 64 controllers, the game is likely Mario Kart 64, though only pure white can be seen on the television screen.
License[]
The creators of Haiyore! Nyaruko-san didn't held any right over Nintendo's Mario, but they only included minor references to the games.