It's been 3 years since I really hit Oil hard. But when I was up that way more it was one of my favorites. Contrary to dfg's experience, it always had EXCELLENT hatches and reliable dry fly action, and was one of the few hatch matcher's delights in the region.
Various Caddis, March Browns, Sulphers dominate the scene. Fishes best in May and usually into early June. In some years it can fish well into July, but it depends on the year and how quickly it warms up.
I'm terrible at identifying different caddis flies. But I can't say I ever really thought it had much in the way of grannoms. Maybe I just always missed em, I dunno. But the major caddis period I've hit over and over is early-mid May. They term it the "mothers day caddis". I think it's perhaps a number of different species, as I've observed green and tan bodies during this supposedly "single" hatch. Like most caddis hatches, rising activity during the hatch can be good, but is hit or miss. Many times wet flies are more effective. Hatch is an early day thing, usually, not evening.
The caddis are followed up by a period where March Browns and sulphers dominate the scene into early June, though the random daytime caddis hatch does still happen. When the water is in good shape, evening spinner falls are reliable and very good.
March Browns in particular. They run late, I've fished spinners as late as June.