The Satcharita talks a lot about Udi. Are there any specific stories about it curing people?

Yes, the footnotes of chapter 33 provide several specific accounts of Udi's healing power, as noted by R. Hari Sitaram Dixit. One story tells of Khimji Lalji Joshi's daughter, who was so weak she couldn't walk. After her mother applied Udi, she felt some relief. When taken to Shirdi, Baba himself applied Udi, and within a few days, she began to walk on her own. In another instance, a friend of Dixit who suffered from insomnia for eight days found relief and slept soundly the very night he took the Udi. These examples from chapter 33 illustrate the tangible and miraculous effects of the Udi.