Non branded, labeled 100% pure extra virgin olive oil, batch number and inventory info.
Anyhoo, get some samples of oil, get some thin non treated open paper.
Cut paper into strips.
Saturate a strip in each type of oil.
Cover the strips in fresh saws dust of the tree types that you would be cutting, make sure saw dust is also oil saturated, rub it in there.
Heat the strips up to the temperature that the sprockets and bar rails cutting surface reach during your average cutting experience, temp gun the parts, surprising variable. Humidity needs to be accounted for, might need to add some water to the oven depending on your climate and wood type.
Cook the strips for the length of time your average cutting experience lasts.
Remove strips from oven and hang near where the saw is stored.
Check on strips periodically until average length of time between saw uses has passed.
Use the oil that corresponds to the most flexible strip, retaining the most saw dust while it flexs. If the dust hardens and falls off it will harden on the chain, bar and saw.
It will help eliminate some choices. Cheapy food grade corn oil and cheapy food grade soybean for example.
In terms of the oil tank, get some containers roughly the same size as the oil tank on your saw.
Fill them up with the average amount of oil you leave in your saw during storage.
Pop a hole in the containers similar to the tank vent in the saw, or just use tank vents.
Toss in some fresh saw dust, if you did not clean out the petroleum oil first put some of that in as well.
Depending on saw, it might be a good idea to heat up the oils to average tank in use temp for the duration of the average use.
Place containers near where saw is stored, check on containers when saw is going to be used.
I used glass containers with plastic lids and tank vents. UV needs to be accounted for if storing in glass containers, most plant oils are not very UV stable, olive oil for example. I was told that the commercial plant based bar oils were also not very UV stable.
Get some weirdo oils, check ph values first...
Go nuts.