I've been having trouble sleeping. Does the Sai Satcharita mention if Udi can help with insomnia?

Yes, Chapter 33 of the Sai Satcharita contains specific accounts of Udi helping people with sleep problems. In a footnote, R. Hari Sitaram Dixit recounts two such instances. In one case, a friend of his had been unable to sleep for eight days despite taking a doctor's medicine. Dixit gave him Baba's Udi, and the very next day, the friend reported that he had slept very well throughout the night. In another similar story, a friend's child from Bandra had not been able to sleep for two months. The father took the child to Shirdi for Baba's Darshan, and that same night, the child got sleep and continued to sleep well from then on.