What is the significance of "va'Yhi bi'Ymei"?
Torah Temimah citing Megilah 10b: We have a tradition from Anshei Keneses ha'Gedolah that "va'Yehi bi'Ymei" always denotes pain. Here, there was a famine.
What do we learn from "Shefot ha'Shoftim"?
Torah Temimah citing Bava Basra 15b: It was a generation that judged its judges. If a judge said 'remove the chip from between your teeth' (fix a small transgression), the person would say 'remove the beam from between your eyes' (fix a great transgression). A judge says "Kaspech Hayah l'Sigim" (there is dross in your silver), and he replies "Sav'ech Mahul ba'Mayim" (the wine that you sell has water mixed in 1 ).
Rashi: This was before Sha'ul reigned. Judges led Yisrael. This was in the days of Ivtzan. Ivtzan was Bo'az (Bava Basra 91a).
Pesichah to Rus Rabah, 1:3: It was a wishy-washy generation. What will I do to them? I cannot eradicate them. Rather, I will afflict them. Vilna Gaon - there is Chesed and Din 2 . Man needs both Midos. Chesed - he must engage in Torah and Avodah and rise in level without limit. Din - he must limit his food and bodily needs, and not fulfill all his desire 3 . Tzadikim - their Yetzer Tov judges them. The Yetzer ha'Ra judges Resha'im; both of them judge Beinonim (Brachos 61b). I.e. Tzadikim's good deeds bring to them influence of great good. Resha'im's deeds cause them evil, until they perish. Beinonim, their deeds judge them with afflictions until their heart is humbled, they repent, and only good remains. Then they merit Chesed Hashem. The generation was wishy-washy (Beinonim) - they turned to good and evil. I cannot eradicate them, for they are not total Resha'im. Rather, I will afflict them with hunger.
Malbim: This tells why he left Eretz Yisrael. "Ein Melech b'Yisrael Ish ha'Yashar b'Einav Ya'aseh" (Shoftim 17:6). Also, when there is one Shofet for the entire nation, he rules over the nation. Here, there were many Shoftim, so people did not fear them - 'if not for fear of the kingdom, man would swallow his colleague alive' (Avos 2:3).
Nachalas Moshe (15a): The latter Aveirah is worse, for he did an action to swindle. Dibros Moshe - the latter is smaller, but since a judge does it, it is worse.
Vilna Gaon: His names are based on His actions. Shem Havayah is Chesed - to constantly do good, even if the recipient is not worthy. Hayah, Hoveh v'Yihyeh - He causes all to exist. Just like He is unlimited, His desire to bestow good is unlimited. Shem Shakai is to limit His influence - He said to His world Dai (enough - Chagigah 12a), and limited its size.
Vilna Gaon: A Mezuzah hints to this. Inside [is Shem Havayah;] man's Neshamah should constantly engage in Torah to fulfill its desire. Outside is Shem Shakai; he must use Midas ha'Din to minimize bodily desires. If he does oppositely, his Neshamah cannot rise. Via Chesed that he does with his Neshamah, he causes Hashem to influence Chesed on the world - "Havi'u Es Kol ha'Ma'aser
Why does it mention that there was hunger?
Vilna Gaon: They did not have mercy on the poor. Hashem gives to a person more than to another, in order that he will have mercy on him and benefit him from his property. They did not do so, so Midas ha'Din overpowered, and Hashem did not influence His good on them.
Malbim: In times of hunger, masses of Aniyim gather to Ashirim and force them to give to them bread and grain - if not, they will take forcibly, since there is no king. This is why Elimelech left - he feared lest Aniyim plunder all that he has!
What is the significance of "va'Yelech Ish [mi'Beis Lechem Yehudah]"?
Rashi (from Rus Rabah 1:4): He was very wealthy and a leader of the generation. He went to Chutz la'Aretz due to stinginess; he did not want to give to Aniyim who came to ask from him.
Vilna Gaon from Bava Basra 91b: Had he found [even] bran, he would not have left Eretz Yisrael.
Malbim: Even though it was a time of hunger and agony, only one man left; the other Ashirim stayed in Eretz Yisrael. Also his household did not want to leave Eretz Chemdah, just he was primary and they needed to go after him. The Midrash says that he was primary, and his wife secondary 1 .
I.e. this teaches that she left only due to him. (PF)
What do we learn from "Lagur bi'Sedei Mo'av"?
Malbim: He did not go to settle permanently, only Lagur, until Hashem's anger passes. He did not go to the city, rather, to the field, like one who goes temporarily.