What behavior does Oswald demonstrate toward King Lear?

In simplest terms, Oswald demonstrates extraordinarily rude behavior toward King Lear.  A pronounced example of this rudeness occurs when Oswald refuses to acknowledge Lear's summons and questions about his daughter in Act 1, Scene 4. A servant's refusal to acknowledge a king's request would have been the height of insubordination, making Oswald's actions very rude indeed. However, he's not just being rude to be cruel; instead, he's acting on Goneril's orders to be rude in order to force a confrontation between herself and her father. Thus, Oswald's actions play a small but important part in the sisters' plans to cast out their father and and gain power over his realms. By this point in the play, they've already received territory from their father by flattering him. As such, all they need to do to rid themselves of Lear is to find a reason to start a quarrel and toss him out into the wilderness. Oswald's rudeness plays a key role in this endeavor.