Oscar would prefer to run away from danger rather than fight it, but he's actually very caring and will do anything to protect his friends from danger. He also admits that he was a nobody until he lied about killing Frankie and he does the same thing when he confesses that he's not a real sharkslayer.
In Shark Tale, he had no qualms about lying in order to make himself appear more heroic and powerful than he actually was. Oscar liked to think of himself as a ladies man, but he was somewhat awkward around females, accidentally bumping into a pillar when trying to seduce Lola and stuttering when he tried to tell Angie how he felt about her.
Oscar quickly became close friends with Lenny and he was romantically interested in Lola, but he eventually realized that she was shallow, vain, vengeful, and selfish. Instead, he fell in love with Angie. He also manages to make peace with Lino after admitting that he wasn't a sharkslayer, thus saving the reef from Lino and his sharks.