1) When the other responders say reset the main breaker, they mean the whole-house breaker - a twin or paired or 2-pole breaker with a bar across the two levers, will be rated for 100, 150, 200, 250, 300, or 400 amps, usually in a separate box. Commonly outside right next to meter box with a separate access panel door (sometimes bottom half of same box) but not always - may be the top 2-pole breaker in your main breaker box - should be labelled Master or Main. Turn off, then back on, making sure you push both levers or tabs together at the same time. If one side flips back off or tries to (do NOT hold it on), then one of the two paired breakers (is actually 2 breakers joined by a junction bar so both trip at same time) may have failed, or you have a short on one side of your circuits that is enough to trip it back out.
2) Check which circuits are not working if your breakers are labelled - if circuits that are controlled by breakers on both feeds of your breaker box are working, then you are getting both sides of the 220V feed from the power company, so the problem is in your house. Try turning off and back on the breakers (as you said you did) for the non-working circuits one by one - may have tripped out some breakers during a surge when the wires went out.
3) To check if one feed wire (one 110V side of the 220V feed) is out - there are two common configurations for breaker boxes. One uses two main bus bars near the center with all the left side breakers feeding off one "side" or 110V feed of the 220V feed, all the right side ones are on the other incoming "live" wire. With this type of box, if one side of the 220V feed is dead, all your dead circuits will be on one side of the box - either left or right. The other type of box, more common I think and more modern, allows 220V circuits to be wired with adjacent breakers on the same side of the box - so one "side" of the 220V volt feed is connected to alternating breakers on the left side (say top, third, fifth down, etc) AND the top, third, fifth, etc on the right side also. The other feed goes to the 2nd, 4th, 6th slots etc on the left AND on the right side. So, if your dead circuits are those that come off all the alternating breakers in the box (all evens or all odds counting from top), then you have that type and again one side of the 220V feed is dead, so most likely a Met Ed line or transformer problem.
4) This is real common in ice storms and high winds and such - the main feed on the power poles usually has 4 wires on a circuit, but only one line breaker will blow on a line that has been crossed with a ground or a tree or such, leaving the other lines live.
5) No real solution for you unless you are an electrician - the immediate solution to at least get het back would be to shut off the power to the house (main breaker), then move the furnace connection (if 110V for gas or oil furnace rather than 220V electric furnace) to a live side breaker of adequate capacity - in the second type box above, easy to do by just swapping two breakers and their feeds. More trouble with first type of box because there will not be enough free wire in the breaker box to do it. Another possibility an electrician might offer as a stopgap would be to disconnect your furnace from the wall feed, put a normal appliance plug on the transformer, and plug that into an extension cord that you would then plug into a "live" wall outlet nearby. Quicker to do, not legal by code as a permanent installation but will work in an emergency as long as your furnace is not electric heat, and is allowed in the general electrical code as an emergency measure, though technically the cord or the circuit breaker would have to have a GFCI (Ground Fault Circuit Interrupter). Many furnaces are rigged this way to disconnect from the power lines to run off a generator or inverter in power outages.
6) An electrician could restore your furnace if it is just 110V to run controllers and ignitor and zone valves and fan and such on an oil or gas furnace - if 220V electric heat would not help any. Might be able to do same with microwave for instance, or other important circuits - but only up to half your total electrical load will be able to be carried. The other stuff you would have to wait for full 220V power - including range, clothes dryer, electric water heater (though in some models you might have half power on 110V), air compressor, welder, electric car plugin for some models, etc.
7) If you do find that it is a one-sided failure, check with neighbors who's power feed comes off a different line transformer to see if they have same problem, then if they have same problem let Met Ed know - that will escalate the repair from a single customer to a feeder line issue, which means it gets higher priority because more customers are on it - also makes it real easy to track down where the problem is, because almost certainly a line breaker or interrupter which is a quick replacement job - typically less than 1/2 hour even from the ground, 5 minutes from a bucket truck.
