Bottle of neem oil is 3 years old, is it okay to use?

According to this source, it should be used within 12 months. This forum also has some helpful information.

It can still work, but is best within about 1 year

The constituent profile of pure neem oil remains relatively stable as long as the oil remains solidified and out of direct sunlight. When subjected to repeated "thawing" to a liquefied state at temps above 60°F, neem oil will deposit a thick black viscous layer called stearin, at the bottom of the drums and containers.

It's reasonable to store neem oil for a year or two, perhaps even three, if a bulk purchase saves money in the long run. Ideally that larger container gets "thawed" but once, at which time the oil is poured into batch size containers. (If you need a quart of neem oil each time you spray, that then is the batch size for your orchard). Liquefy each batch gradually by bringing it out of cool storage the day before it's needed, and if it's still gunky in the morning, stick the jug in a pot of warm water for an hour or two. Don't use very hot water as this will reduce the effectiveness of the oil.