Here's possibly a little flight of fancy or possibly an explanation...

If "oil of green" is short for "oil of wintergreen", it's conceivably a reference to a particular leather, or a colour from natural dye. I searched on "fabric dye" and "oil of wintergreen" and came across the following:

Family Betulaceae Birches
order: Fagales
•Betula ◦B. lenta Beech, Cherry Birch - source of 'oil of wintergreen' (actually oil of birch)
◦B. pendula Silver Birch - sap used for syrup, wine and vinegar; tar used for dressing Russian leather; leaves used medicinally and for dyes; oil used for medicated soaps

I understand from past reading about herbs and natural dyes (too long ago to recall specific sources) that lower-grade results were/are often available by using related plants, which was/is done if the ideal plant was/is unavailable or too expensive. And plant both common and scientific plant names vary over time and geography, so "oil of (winter)green" may have had variant meanings over time and geography too.

url for the page is http://www.campin.me.uk/Food/related-plant-list.html (Small world, looking up something to inform my post on mudcat and getting a web result to Jack Campin's page.)

Of course if the words really aren't "oil of green" or if they aren't short for "oil of wintergreen", then none of the above is relevant.