Nurarihyon no Mago, Dororon Enma-kun Meeramera Recommendations
Both male leads defeat youkais, and said male lead isn't human, along with a lot of the other cast. One of the female leads are humans and is involved with the male lead. The male lead is extremely overpowered, but rather stupid. The said male lead is involved in a demon patrol, but that male lead is the only one who can actually fight. There is a person who uses ice to defeat youkai in both anime.