1. Compare and contrast the conditions at the court of Odysseus at the beginning of The Odyssey with those of Nestor and Menelaus when Telemachus visits them. How do these contrasts illustrate the theme of order vs disorder in The Odyssey?

In the first four books of The Odyssey, Homer builds the world into which Odysseus will be returning at the end of his journey: the situation in his own kingdom is vividly illustrated, as well as its impact on his wife and son, and this is neatly contrasted with the situations in the kingdoms of Nestor and Menelaos. In their kingdoms, all is beauty, grace, harmony, and hospitality, while in Odysseus's kingdom, unwanted guests plunder his wealth, bully his son, and harass his wife for years on end, to the despair of his servants and subjects.
We are first introduced to Telemakhos by the goddess Athena, who has come to the palace in disguise to assess the situation. Telemakhos is sitting forlornly in the palace courtyard, while around him the suitors make free with the household resources as if they own the place:

Before her eyes [Athena] found the lusty suitorscasting dice inside the gate, at easeon hides of oxen—oxen they had killed.Their own retainers made a busy sightwith houseboys, mixing bowls of water and wine,or sopping water up in sponges, wipingtables to be placed about in hall,or butchering whole carcasses for roasting.

The suitors are immediately shown to be boorish, ignoring Athena as she stands on the threshold of the palace, in contravention of the rules of hospitality. Telemakhos is the first to see her and is embarrassed to see how a potential guest has been treated:

Straight to the door he came, irked with himselfto think a visitor had been kept there waiting[.]

He brings Athena into the palace and treats her with all due courtesy, despite not knowing who she is. He is annoyed by the suitors' behavior and does his best to make up for it, arranging a separate seating area for himself and his guest, for:

To be amid the din, the suitors’ riot,would ruin his guest’s appetite, he thought[.]

Athena comments on the suitors' behavior, saying:

"How arrogant they seem,these gluttons, making free here in your house!A sensible man would blush to be among them.”

Telemakhos bitterly agrees:

"[They] eat their way through all we have,and when they will, they can demolish me.”

It is evident from various things—the painted chairs, the gold and silver serving dishes, the abundance of food and wine—that Odysseus's household still possesses great wealth. However the situation there is loud and chaotic; all semblance of household routine has been thrown over in favor of the suitors' desires on any given day. They do not honor the rules of hospitality with regard to outsiders, and they do not honor their host. When Telemakhos first tries to assert his authority, they taunt him and don't take him seriously. When he asserts it more forcefully, they plot among themselves to murder him. This is such a severe breach of ethics, it's staggering. Obviously murder in any context is a terrible crime, but to murder their host constitutes such a major violation of the sacred contract of hospitality, it's almost beyond belief, and this underscores how anarchic the situation in Odysseus's court has become.
Contrast this setting—a loud, messy environment not unlike a fraternity—with the kingdoms of Nestor and Menelaos. The first impression Telemakhos gets of Nestor's kingdom is one of communal religious piety, as Nestor and his sons preside over a sacrifice to Poseidon. They immediately extend their hospitality to the young man and his companion (Athena, still in disguise):

When they saw the strangersa hail went up, and all that crowd came forwardcalling out invitations to the feast.

Nestor is a kind and gracious host. He offers Telemakhos all the information he can provide on Odysseus and sympathizes with his situation. He insists that Telemakhos stay with him at his palace for as long as he likes, and he won't hear of the boy staying anywhere else:

"Zeus forbid, and the other gods as well,that you should spend the night on board, and leave meas though I were some pauper without a stitch,no blankets in his house, no piles of rugs,no sleeping soft for host or guest! Far from it!I have all these, blankets and deep-piled rugs,and while I live the only son of Odysseuswill never make his bed on a ship’s deck— no, not while sons of mine are left at hometo welcome any guest who comes to us.”

When Telemakhos leaves to visit Menelaos, Nestor provides him with a beautiful chariot and two of his best horses, as well as the company of his son Peisístratos, to help and guard him on his way. All has been done in accordance with the sacred rules of hospitality and with genuine warmth and good-feeling. Nestor's children love and respect their father, who in turn cherishes them and his entire kingdom. The community is close-knit and harmonious.
Things are similar at the palace of Menelaos, and Homer points out the ill behavior of the suitors by showing one of Menelaos's guests, Eteóneus, unsure whether to admit the young men to the court. Menelaos strongly admonishes him for his failure to be hospitable:

“You were no idiot before, Eteóneus,but here you are talking like a child of ten.Could we have made it home again—and Zeusgive us no more hard roving!—if other menhad never fed us, given us lodging?Bring these men to be our guests: unhitch their team!”

This palace, like Nestor's, is a beautiful and welcoming environment:

What a brilliant placethat mansion of the great prince seemed to them!A-glitter everywhere, as though with fierypoints of sunlight, lusters of the moon.The young men gazed in joy[...]

Telemakhos remarks to his friend:

"This is the way the court of Zeus must be,inside, upon Olympos. What a wonder!”

It is a peaceful place, where King Menelaos and Queen Helen rule their subjects generously and are rewarded with their love and loyalty. Like Nestor, Menelaos also gives Telemakhos all the information he can about Odysseus, and he prays for Odysseus's swift return to Ithaka. Like Nestor, he insists that Telemakhos stay with him, enjoying his hospitality, but Telemakhos declines, citing the need to return before the suitors wreak more havoc. Menelaos then offers him a parting gift:

"Let me see what is costliest and most beautifulof all the precious things my house contains:a wine bowl, mixing bowl, all wrought of silver,but rimmed with hammered gold. Let this be yours.It is Hephaistos’ work, given me by Phaidimos,captain and king of Sidon. He received meduring my travels. Let it be yours, I say.”

Telemakhos leaves the court of Menelaos as he left the court of Nestor, with gifts and good wishes, having established a strong bond with his host.
The world of Nestor and Menelaos is the world Odysseus deserves to return to, with a happy family, fertile lands, and a peaceful home. Nestor and Menelaos also served ten years in the Trojan War, but they made it home afterward and were able to re-establish themselves as rulers in their kingdoms without issue. Their absence was not sufficiently disruptive to allow disorder to encroach on their spheres of influence.
Odysseus, by contrast, has been gone for so long that his kingdom has fallen into a kind of social disrepair: the resources are still there, his family still loves him, and his subjects are still loyal, but in his absence, other interested parties have begun to appropriate Odysseus's things to themselves. Order can only be reasserted in Odysseus's kingdom by his return, which should restore society to its proper settings.