Hello Ina, sorry to hear of your Mother-in laws diagnosis and surgery.
A ventilator/respirator is a machine that breathes for the patient when they are unable to do so themselves. Either because they are sedated/unconcious or they have muscle paralysis.Usually after an operation it is because they are sedated.
It is normal for the oxygen to be weaned according to the patients oxygen saturations - this is a measurement of the percentage of oxygen in the blood. Depending on chronic lung problems the patient may have, anything over about 95% is good.
You and I breathe in atmospheric oxygen which is 21% so your Mother -in-law having 24% O2 is about back to normal.
You say she has a tube in her mouth? This could be the endotracheal tube that was used to ventilate her and they could well leave this in place, but not attached to the ventilator ,until they are confident that there is no longer any throat swelling. It would be normal to attach oxygen to this oral endotracheal tube. Did she not have a tracheostomy?
Once the endotracheal tube is removed she would be able to move to a regular room.
Hope this helps. Sounds like she is doing okay.
Tammy

Caregiver/advocate to Husband Kris age 59@ diagnosis
DX Dec '10 SCC BOT T4aN2bM0 HPV+ve.Cisplatin x3 35 IMRT.
PET 6/11 clear.
R) level 2-4 neck dissection 8/1/11 to remove residual node - necrotic with NED
Feb '12 Ca back.. 3/8/12 total glossectomy/laryngectomy/bilat neck dissection/partial pharyngectomy etc. clear margins. All nodes negative for disease. PEG in.
March 2017 - 5 years disease free. Woohoo!