Innate = born with it. My friend has an innate talent of singing. Homosexuality is innate, it's not a choice. Intrinsic = A fundamental, natural part of something. Empathy is intrinsic to human nature. Gravity is an intrinsic part of the universe.
"innate" is almost always used to describe an ability and only used with animals, particularly humans. It suggests that one did not have to acquire/learn that quality. It typically wouldn't be used to describe a computer or a robot.
"inherent"/"intrinsic" are generally used with objects or abstract concepts. They can mean "built-in" or even "by definition". "This method has an intrinsic advantage." "Diamond has intrinsic value because of its extreme hardness."
In other words, without that quality, the thing would not be what it is. "The crystalline structure of diamond is an intrinsic property."
Sometimes "intrinsic" is used simply to mean "internal" as opposed to "external".