Image courtesy: Brig A.P. Singh - www.collectingmoment.in
Hoysaleshwara temple is dedicated to Lord Shiva hence the easy conclusion would be that this sculpture is of Shiva and Parvathi. However, looking at the statue, the male deity here is holding the Conch shell (Shankha) and Chakra (discuss) which means it is Lord Vishnu. Hoysala royals were known patrons of Lord Vishnu but both Shaivism and Jainism thrived under their support.
Image courtesy: Brig A.P. Singh - www.collectingmoment.in This statue is broken at the hands making it difficult to identify the deity. However, we can infer that the right front hand of Shiva is holding the damaru - a small drum - one of Shiva's signature items. And the back left hand could be holding the Trishula.
Image courtesy: Brig A.P. Singh - www.collectingmoment.in [Though it is a damaged sculpture, we can identify the gada (mace) and shankha (conch) on the two left hands of Vishnu.
Image courtesy: Brig A.P. Singh - www.collectingmoment.in Kali, a fierce form of Parvathi, is seen here with a trident, skull on a stick and is dancing on a corpse. Kali was born out of Parvathi when the demon Rakthabeejasura needed to be slayed.