Dug up my badly decayed and falling apart copy of the Lostech equipment guide (please Catalyst, PLEASE make it available in PDF at some point! I will give you moneys for it!).
Long story short, For the most part they essentially function as conventional infantry armor that provides a significant bonus to strength in exchange for a degree of automatic encumbrance. The light exoskeleton is automatically encumbering, while the industrial exoskeleton is automatically very encumbering. Those familiar with the armor stacking rules in A Time of War and the infantry armor rules in Tactical operations will note that this places some inherent limitations on their battlefield utility. The Light exoskeleton could be considered technically viable, but it provides basically no additional protection (you'd be limited to whatever armor you're wearing under it), and really, at total warfare scale, it's not going to change anything. Essentially, as Sillybrit said, you might as well assume that they are used by anybody who has to carry a load on the wrong side of ridiculous.
Under A Time of War rules, the high natural encumbrance of the Industrial Exoskeleton basically prohibits the use of any additional body armor. The Exoskeleton DOES have its own armor ratings, but they aren't high enough to warrant a Total War damage divisor higher than one, making the industrial exoskeleton inherently inferior to practically any other infantry armor option.
The heavy industrial exoskeleton is a special case, as it isn't used operated like the others in the RPG scale. It has a fixed maximum speed (3.6 kilometers per hour), and a fixed lifting capacity (2 tons). It has an inherent armor rating sufficient for a damage divisor of 2 on the total warfare scale. Also, it drains power very quickly. A high capacity backpack power pack will be completely drained in five hours of operation, which just adds to the logistical tail (the other exoskeletons have operating times that seem roughly comparable to battle armor). It's not "encumbered", instead being classified as a "vehicle", and those lifters are probably not suited to operating infantry weapons.
One could make the argument that the Heavy Industrial Exoskeleton might be jerry rigged for combat (in fact both I and the Canon have made that exact argument), but all the mentioned limitations means it's not something you should expect often.
Oh yeah, all of these can be environmentally sealed and rigged for zero g operations. Based on how they operate, however, that's not really any different from the marine environmental armor or combat spacesuit.
