The oven-baked oil finish.
This uses Charles' Law of Physics: gases expand as they are heated and gases contract when they are cooled.
Preheat your kitchen oven to 325F/165C.
On a mesh pastry rack over a sheet pan, brush your wood carvings wit the vegetable oil of your choice.
I use olive oil as I have many liters of it in my kitchen.
Into the oven for 3 minutes and 30 seconds by the clock.
Take the tray out and look at your wood carvings, the end grain. See all the little wood air bubbles?
Now as the wood cools, the remaining wood air will contract and suck the oil down into the wood .
You can always brush more oil on the wood at this time I did that, some times.
When cold, wipe off the excess oil and you are done forever. That oil cannot be washed out or cooked out
unless you heat the wood to more than 165C again.
You asked about doing this to stained wood. I do not know the answer. You do the experiment and tell the rest of us.