All four forwards spent most of last season in the AHL with the Kings' Manchester affiliate, but all four also played for Los Angeles.
The Kings announced the deals Saturday night, a few hours after avoiding arbitration with center Brad Richardson by signing him to a one-year deal.
Clune had two assists and 26 penalty minutes in 14 games with the Kings last season, also appearing in four playoff games.
Lewis, a first-round pick in 2006, started the season with Los Angeles, and Elkins scored his first NHL goal while playing in three games with the Kings last season. Cliche made his NHL debut in March.