Can my home's power supply handle this tankless water heater?
Well, to simplify the maze somewhat, you have all the usual loads of an all-electric house. 


50A furnace
50A range
30A air conditioning pack
30A dryer
Eleven 120V branch circuits, some MWBC, many on 30A breakers (WTH?) 


Obviously we can oversubscribe this somewhat, e.g. You're not likely to run heater and A/C at the same time. 

The fine art of panel subscription is not a core skill for me, but hopefully this summary will make it easier for someone else.  

That panel, though

While we're here, we gotta talk about that panel.  First,  panel B top-tapping panel A before the main breaker is very dangerous unless there is another main breaker before this.   The meter is not a fuse, and there are no fuses between the transformer and main breaker. This is considered acceptable for a very short hop from the meter to the main, however, in your case this totally unfused feeder crosses your whole house.  Nothing prevents a short in the cable, or in this panel, or summed loads on this panel, from setting that cable on fire.

Second, all 4 panels are Federal Pacific "StabLok".  It has serious issues with panel fires due to bus defects, and unreliable trip. When feasible, all four should go.

The three subs will be straightforward to DIY, the main will be more troublesome unless there's an outside main breaker.  I would DIY install a 200A main service panel right next to it as a subpanel, reuse that 70A breaker to feed it, and move all the 120V circuits out of the main into the new sub.  Then bring in an electrician to cut it over to be the new main.  

I see many branch circuits on 30A breakers. Those should be 15 or 20 depending on wire gauge.  

Gaps in the panel covers should be patched so curious fingers can't touch buses, except finding either breakers or blanks to cover those spots will be a pain.