The triage call runs a fixed sequence: fuel type (gas or oil — each routes differently, and oil is common enough here to ask about first), what failed (heat, hot water, or both), error code if the display shows one, how fast it is getting cold inside, and your ZIP. "Oil, no heat, red reset button lit, house at 57 and falling, 11580" gets you correctly prioritized in under a minute.
For oil homes, two extra answers help enormously: the tank gauge reading — a run-out is a delivery plus a bleed-and-reprime, a completely different dispatch than a dead burner — and when the burner was last serviced. Be honest about renters vs. owners too — if you rent, the property owner usually needs to authorize work, and the triage will tell you that upfront rather than after a truck rolls.