Yes, there are still indulgences, and they are still obtainable. I’m guessing that the priest’s statement stemmed from him not understanding your question.
The Church document concerning indulgences (both plenary and partial) is called Enchiridion Indulgentiarum: Normae et Concessiones.
As an example of how the Church still promotes the practice of indulgences in modern times, in 2000 the Vatican ascribed a plenary indulgence to certain devotions in conjunction with Divine Mercy Sunday. Please see this Zenit article for more details.
My guess is that perhaps the priest thought of indulgences in the Medieval sense of the word. My understanding is that, back then, the rich and the powerful could “purchase” indulgences for their sins. It was a controversial practice for “fund-raising,” so to speak. The priest may have wanted to emphasize that this form of indulgence is no longer practiced.
DISCLAIMER: Catholic Answers has turned over the archive to Catholic-Questions.org and no longer owns, manages, or moderates the forums. For additional apologetics resources please visit www.catholic.com.