Lords remaining behind to guard castles is kind of a toss-up. If one lord's party was particularly chewed up in the fighting, he'll decide to call it a week inside the castle they just sacked. If they're all generally healthy, they'll just move on.
Anyway, the two main constants for sustaining morale are Leadership and food variety. Food variety can be extremely expensive to handle if you don't have good Looting - with good Looting, you can just save some leftover suits of armor or swords and barter them for food. Don't overlook hardtack; people will eat some hardtack even if you have much better food and stretch the variety bonus longer.
Truthfully, the way I have dealt with it in my most recent game is to get very high agility quickly (I started the game with 21), pumped agility to 27 and took 9 Looting. Then I pumped Cha up to 27 and took Leadership up to 9. Then I bought Life of Alexinus The Great, which gives +1 leadership when read. While reading the book, I bumped agility up to 30 and maxed out Looting (and Riding).
I get so much crap now it's not even funny. Any one suit of armor I get from a fight is more than enough to wipe out any merchant's cash reserves. When buying food, butter, cheese, and ale/wine from the village elders, I just give them a sword or the 80th 'reinforced great helm' i got from mercenary war parties, so keeping a big variety of food is literally cost-free. Even at 303 men, the only time I have morale problems is right after recruiting 30+ prisoners.