These three words are very similar in meaning, and to be honest, I rarely hear any of them in everyday, spoken English.
But it comes down to what you are describing by each of the three words.
Innate usually describes an ability of a person. You might hear: “She has the innate ability to learn languages quickly and easily.”
Intrinsic usually describes describes the value of something. You might hear: “Even though she doesn’t earn much money as a teacher, the intrinsic value of her job is extraordinary.”
Inherent usually describes a quality or component of a thing, not a person. You might hear: “The possibility of severe injury or death is an inherent risk in skydiving.”
Hope this helps!