Omeruo was handed a starting role while Awaziem came off the bench to help the Cucumber Growers end a five-game losing run at Mestalla.
The visitors started the match on the back foot after conceding a penalty in the 21st minute, which Dani Parejo calmly dispatched for the opener.
In the 35th minute, Oscar levelled for Mauricio Pellegrino’s men to ensure his side avoid defeat for the first time this season.
Omeruo featured from start to finish in the encounter while Awaziem replaced Aitor Ruibal in the 57th minute.
Despite the draw, the Cucumber Growers remain at the bottom of the table with one point from five games.
Leganes will hope to clinch their first win of the season when they take on Athletic Club in their next league game on Wednesday.