All of these terms are used interchangeably, so the following definitions probably wont be too helpful in the real world, but in my experience:

Artificial Intelligence is an umbrella academic term which encapsulates the study and design of intelligent machines. It's not well defined because AI is evolving so rapidly.

Machine Learning is a branch of AI that is concerned specifically with learning from data; the results of learning are usually used to predict future events. (Think linear regressions, random forests, etc.)

Though not specifically a part of AI, Statistics is the field that formed many of the algorithms used in ML. Stats informs ML research design (e.g., how large of a sample size do I need), generates mathematical solutions from proofs and equations, etc. With the rise of big data, it's slowly merging with ML.

Data Mining is a mix of ML, Stats and Data Engineering. It's more concerned with structuring and extracting patterns from data than necessarily learning from it. It is often a task within an ML project.