How big of a Battery Backup or powerwall do i need to power 3 medical devices
The first rule of off-grid power is

Conservation first.

The second rule of off-grid power is 

Conservation first.

You do not, do not, do not, under any circumstances, use an inefficient old piece of junk just because you already have it.  Nor do you spec and acquire new equipment without thinking hard about efficiency and practicality of battery power. 

As an example, suppose you have a server you want on a long term battery backup.  You're using an old gaming PC with dual Radeon 980s and an 850 watt power supply (so 1200 watts practical).  Do you a) install $12,000 of battery and charging apparatus, or b) buy a Mac Mini for $1200 that draws 40 watts, and fit $400 of battery and charging apparatus?  $12,000 vs. $1600. Tough call. 

But this is just the kind of blunder that people stumble into when they are new to the idea of battery backup/off-grid power.

So this is a frame challenge.  Stop wasting your money and our time trying to power the equipment you've got.  It's way cheaper to replace with efficient equipment than to power your old stuff. 

The third rule of off-grid power is 

Inverters suck. Get DC versions of things.

The best way to power equipment is straight off the battery.  This avoids power conversion which is extremely inefficient, forcing you to triple or even quadruple battery/charging. *

I happen to know many CPAPs are produced which use 12 volts natively.  They might plug into the wall, but it's via a "power brick" or "wall wart" power supply which turns mains voltage into 12 volts for the machine's actual use.    And by the way, 180 watts is a ludicrous amount of power for a CPAP.  There is something wrong with that spec - it may be the spec rating of the DC power brick.  

Sometimes you cannot avoid running an inverter.  In that case, you manually spin up the inverter only while you are actively powering a thing that needs it.  That is the way to handle the oxygen pump if you can't get a DC version.  So in that case you do need to account for inverter losses, but only when the unit is running.  

We're not a shopping site, least of all for medical equipment, so I leave it to you to do your research.  



* "But surely inverters are more efficient than that!" Not when your loads are cycled off, they're not. You have a 200W load that cycles 10% of the time, like a fridge.  At that load the inverter is 80% efficient, so for 1 hour, it takes 250 watt-hours.  The other 9 hours the inverter draws 60 watts standby, or 540 watt-hours.  That's 790 watt-hours when you only actually use 200.  That's 25% efficiency where I come from.  That's why inverters suck.