No. Osmium cannot replace Calcium
Osmium tetra oxide is highly poisonous, so you would have to rearrange human biology to avoid that issue. Nanotubes made of Osmium, carbon and iron don’t sound very likely either. I think you are trying to fit too much functionality into this exoskeleton. It would be much easier to use magic and be done with it.
Osmium's extreme density would also make it extremely unwieldy. A body armour surface area of 2 square metres coated with 1mm of Osmium would weigh 45kg