Mix = using a utensil to stir the ingredients together. blend = using a machine like a Blender to combine ingredients together. intermingle = to mix people together. At a party or meeting. Each of these can be used as a metaphor for people at a party. "We have a good mix of people at this party." "Ya, it's a good blend of different people." "And they are all intermingling so well."

I think as verbs they can be used mostly interchangeably. But there are some subtle distinctions. Mix and blend usually refer to when two or more things are put together in such a way that they are no longer separate. Intermingle suggests that there is something about the parts that you can still see as separate.