What are the similarities/diferences between the homecoming of (Menelaus, Agamemnon and Telemachus) to Odysseus? And does it have an importance?
As others have pointed out, one major difference between Odysseus's and Agamemnon's reunions with their families is that Agamemnon returns to an unfaithful wife, Clytemnestra, and her lover, Aegisthus. These two have plotted to murder him in his absence, and they do so when he returns. His son, Orestes, grows up, however, and eventually kills both his mother and her lover in order to avenge his father. Orestes is thus held up as an example of a good son, one who honors his father above all else, and Clytemnestra is considered an example of a terrible wife who lacks obedience and loyalty to her husband.
Thus, Penelope has a model for how not to behave in her husband's absence. Much is made of her loyalty to Odysseus, despite his twenty-year absence and the fact that she's had no credible news of him during that time. We can contrast the upright behavior of Penelope with the deceptive and dangerous Clytemnestra, throwing into even starker relief just how good Penelope is considered to be in ancient Greece. Telemachus also has a model in Orestes, though he is a positive model for how to be a good and loyal son to Odysseus. When Odysseus first returns home, he does so in disguise, and only his son knows who he is (for a while). He doesn't go right up to his own house, as Agamemnon did, because he knows the suitors there will kill him immediately. He plots carefully, even keeping his identity secret from his wife until he can test her loyalty to him. In short, the contrast between Penelope and Clytemnestra and the similarities between Telemachus and Orestes help to show us which qualities are not desired or desired, respectively, in wives and sons. We also see, by the way Odysseus chooses to return home, that he might be a bit more circumspect and strategic than Agamemnon.
When Menelaus returns from the Trojan War, he is victorious and has reclaimed his wife, Helen. Helen had been an unfaithful wife, unlike Penelope who remains faithful to Odysseus for the entire twenty years he is gone. Menelaus has forgiven an unfaithful wife, while Odysseus can rejoice in a loyal wife.
Agamemnon is murdered by his wife's lover upon his return from the war. This disloyalty is avenged by Agamemnon's son when he kills his mother's lover. Again, Odysseus has a failthful wife (unlike Agammemnon), but he DOES have a loyal son (like Agamemnon).
Telemachus is always loyal to his father even though he has not seen him since he was an infant thown in front of a plow. His loyalty to his father makes him a threat to the Suitors, and so they wish to get rid of him. When he returns from visiting Menelaus, the Suitors, led by Antinous, plot to murder him. He is not shown proper respect as the son of the King of Ithaca.
When Odysseus returns, he comes in disguise to learn who has (and who has NOT) been loyal to him during his long absence. Unlike the others, who come home as "themselves", Odysseus uses stealth before announcing his arrival. This prevents him from being killed, like Agamemnon, by someone who wishes to steal his wife.
Odysseus arrives home to find a faithful wife waiting for him. Agamemnon, on the other hand, arrives home to an unfaithful wife and together with her lover they plot and murder Agamemnon.
Odysseus arrives home with nothing from his journey except glory and pain. Menelaus, on the other hand, arrives home with so much wealth. He obtained the wealth from foreign lands after a detour from his journey back home.
The similarity between Menelaus and Odysseus is that they both get to stay with their wives after they arrive back home. Menelaus arrives with his wife from Troy, and Odysseus meets his wife waiting for him.
Telemachus, Agamemnon, and Odysseus had enemies plot their death as they traveled back home. Telemachus and Odysseus had the suitors to contend with, while Agamemnon fell into Aegisthus’s trap.
Odysseus’s look gave him enough time to plan his revenge on the suitors. Thus, it was important how Odysseus arrived back home and how he conducted himself before the suitors.