The tree is a symbol, ultimately, of the natural order of Agamemnon's rule, so violently corrupted by his murder and the usurpation of his power. Electra refers to Agamemnon as an "oak" cut down by Clytemnestra and Aegisthus several times throughout the play, and the tree that grows from Agamemnon's scepter in Clytemnestra's dream is a clear omen of the restoration of natural order to be brought about by the return of the legitimate heir, Orestes.
The doorway, or threshold, is symbolic of the division between honor and dishonor, good and evil, light and dark. It is where Electra spends all of her time, half inside, half out on the street, as if waiting to bring goodness (Orestes) inside to purge the evil (Clytemnestra and Aegisthus). Yet as the play progresses and Electra loses her grip on rationality and the morality of the revenge comes into question, the distinction between inside and outside is fittingly blurred. Aegisthus, at the very moment of revenge, demands that the gates and doors be opened wide, in effect erasing the doorway as the lines between moral and immoral fade with the exaction of revenge.
Throughout the play, Electra's intense desire for revenge is symbolized as a knot—one that no one, she claims, can untie, as it grows tighter and stronger with each passing day that she must live amongst evil and corruption. Revenge alone does not suffice, either. Electra demands the desecration of Aegisthus's body and the prohibition of his speech, or the violation of justice, as the only conditions under which the "knot" of evil inside of her can be loosened.