They indeed are all very similar. They also aren't used very often and I suspect if I went to my native speaking coworkers and asked them the definition of 'acumen' most would not know the answer :) But to answer your question. Acumen- generally refers to good decision making and skills. For example, the lawyer is known for his legal acumen. Acuity - is used in a more broad sense so that it can cover things such as senses or general wit and intelligence. For example, the cats visual acuity is much better than humans. Acuteness - This is even more broad and can actually be confusing since 'acute' can be used in math, describing a symptom or wound or a skill. Examples: The acuteness of the angle confused the teacher. The doctor analyzed the acuteness of the injury and determined it occurred during the car crash. The football players acuteness helped him score.

http://www.softschools.com/difference/acumen_vs_acuity_vs_acuteness/199/