The Oath Rod might be a form of compulsion, that settles into the brain, or even more refined into the cns. Thus the choking effect that we see from Siuan in New Spring. In effect a mini seizure.
I think that it also does damage to the cns as well with each oath taken.

Like many things such as cigarettes, alcohol, etc. the effect on the body isn't instantaneous, but becomes readily apparent after an extended period the ageless look is a side effect of the damage, with the life span being decreased dramatically.

As for stilling...I think that when the ability to channel is taken away, it unravels the Oaths...undoing the neurological damage in the process.

As for removing the Oaths on someone close to their 300 anniversary, I doubt it will have much effect on their longevity. It might add a few extra years, perhaps more...but overall I doubt it will add back the entire channeler's lifespan. At most a few decades I think.