What are the differences between the Army ESEO, Air Force Public Health Officer, and Navy EHO?

There’s a lot of responsibility overlap. However, the primary differences are: an Army ESEO performs both public health and industrial/occupational hygiene functions, whereas the Navy splits Environmental Health and Industrial Hygiene into two separate Officer career fields. The AF does something similar, having a Bioenvironmental Engineering Officer overseeing IH, and a Public Health Officer doing traditional PH. Thus, the Army route essentially wraps everything into one MOS. The other branches break them apart into separate jobs.

They are pretty much similar positions. Army supports health and safety for garrison and combat units during peacetime keeping missions, humanitarian assistance. Air Force cover all aspects of public health from disease surveillance to health promotion and administration. Navy, safety of citizens towards disease prevention, emergency response and preparedness.