Koly gets her strength from a combination of sources. One such location is from her own sense of self. In the opening lines of the book, we are made aware of the idea that Koly does possess an internal strength when she argues that her departure into the unknown world of marriage as a child, "will make room for everyone else." With this quote, we get a good idea of the fact that Koly possesses an internal strength that makes her strong enough to endure what will lie ahead.
Additionally, Koly gains strength from the sanctuary in Vrindavan. While she is abandoned there, she also gains strength from the fact that she no longer is going to be tormented by her mother in law. Being abandoned might have been scary for her, but we see that in this wide scope of freedom, she possesses the ability to define herself and change her own sense of identity. This requires strength, and in the process of gaining economic independence and personal independence we see that she is able to use her freedom and turn to it as a source of strength. The final location from where Koly might derive her strength is from her own experience as a woman in the traditional realm of India.
The common perception is that traditional Indian women are subjugated, and thereby weak. I would posit that Koly's characterization (as well as the millions of other women like her in India) challenge this assessment. Being a child bride in the traditional cloisters of India causes Koly to grow up quickly and assume a great level of strength. Being married under false pretenses, becoming a widow far too soon, living life under the despotic tyranny of a mother in law, all before the age of 30 (being very liberal) teaches a woman to possess a great deal of strength. It is from this reservoir where Koly draws, like water from a well, to endure difficulty and eventually triumph over it.