What sort of emergency situations are covered by out of network insurance?

what sort of emergency situations are covered by out of network insurance?

Only what your policy states. There isn't a universal answer.

Smoothie is exactly right.
However, I happen to have a booklet here that includes some of the typical language used by one of the many companies that can be selected as part of a menu of health plans.

This is just one example of many types of requirements that MIGHT be in a randomly selected plan:

"*** Emergency services or medical emergency is
defined as: health care services that are provided
in a hospital emergency facility after the sudden
onset of a medical condition that manifests itself
by symptoms of sufficient severity, including
severe pain, that the absence of immediate
medical attention could reasonably be expected
by a prudent layperson, who possesses an average
knowledge of health and medicine, to result in:
• Placing the patient’s health in jeopardy;
• Serious impairment of bodily functions; or
• Serious dysfunction of any bodily organ or
part. "

Just some general info and of course not likely to be the language used in the plan you might have or might be considering.