What is the virtue of the Udhiyah (sacrifice) for an unmarried woman, and which is better in her case: giving charity with money or offering the Udhiyah, especially since her income is modest?

The Udhiyah (sacrifice) is a confirmed Sunnah according to the majority of scholars for whoever is able to perform it, whether male or female, provided they are free (not enslaved). Performing it is better than donating its value in charity.