Work is permitted on Chanukah but eulogies and fasting are prohibited all eight days. If a scholar dies, though, he may be eulogized during Chanukah.
The Maharil writes that it is a tradition that no work is done while the Chanukah lights are burning. An allusion to this can be found in the name of the holiday: Chanukah – chanu ["they rested", from their enemies and from work].
It is a custom that women do no work as long as the lights are burning, and they should not be lenient in this matter. Among some Sephardic communities, women refrain from work all day during Chanukah. In other communities, this custom is followed only on the first and last days.
The reason for particular emphasis of Chanukah observance on the part of women, is that a harsh decree had then been issued against the daughters of Israel: The Greeks ordained that every girl who was to be married was to be brought first to the Greek ruler.
Additionally, the miracle itself came about through the heroism of a woman. The daughter of Yochanan the High Priest was especially beautiful, and the Greek tyrant king desired her. She pretended to acquiesce, came to him, and fed him cheese dishes until he became thirsty. Then she gave him wine to quench his thirst, and he became intoxicated and fell asleep, whereupon she beheaded him. She brought his head to Jerusalem, and when the enemy commanders saw what had happened, they fled. It is said that this is the reason for the custom of eating foods made with cheese on Chanukah.