Pattee,
I would leave a few on the trees (1 or 2 older figs) just in case the weather stays warm.
I have followed Martin's and Herman2"s advise since last year, and I have been able to taste ripe figs from most of my plants, by removing all the figs that do not stand a chance of getting ripe.
Since it takes 90 -120 days for figs to ripen from the embryonic stage, you can remove any figs that will need more time past your first frost date (if they were formed after July 7), some cultivars are at the beginning (Celeste, Improved Celeste, Italian Honey) and some are at the end (VDB, Scotts Black, Green Ischia, Papa John). Since the weather has been relatively warm in the daytime, we may have another 2-3 weeks. The colder night temperatures (High 30's to 40's) have not stopped the figs from ripening at my location, and you are usually warmer. I'm still harvesting Hardy Chicago, Papa John, VDB, LSU Gold and a few unknowns from 2 year old and younger trees.
BTW, oiling only works if the figs are near the end of their ripening cycle (90 - 120 days).