Oslin never married during the course of her life. However, she did have several long-term relationships through middle age. This included a several-year relationship in the 1970s with Alan Rubin. Rubin was a musician and former member of The Blues Brothers. The couple lived for two years in upstate New York in a rural community. The relationship would dissolve after two years and Oslin moved back to New York City. It was Rubin who gave Oslin her first piano following their separation. Oslin would dive into songwriting following her breakup: "That pulling back period is when I started to write." Oslin later dated record producer Steve Buckingham and drummer Owen Hale. However, these relationships eventually ended. "I’m alone, but I like my own company," she told "People" magazine in 1993.