You can say that machine learning is probably the most homogeneous of these three terms, and the most commonly used. The machine is all about training models, applying various applications, and predictions.
Machine learning is mostly used for research, automation, and much more.
Information Retrieval and Data Mining are much more alike in describing complete commercial processes (Business Analytics), it is all about user query to retrieval/delivery of related results. ML algorithms might be somewhere in that process flow, it makes sophisticated applications work more smooth by automation.
I hope this answer helps.
Also, if you are willing to learn about training models, applying various applications, and predictions in ml then you should enroll in ML training.