What is the best way to check airfares for multiple airlines?

https://www.google.com/flights/

I like Momondo.com slightly more than google flights.

Just Google ITA Matrix. It's a comprehensive website for industry insiders. You cannot buy the tickets there, but it'll route you to the best solutions for your flight.
If you can fly out of Orlando, look no further. Norwegian Air Shuttle is the cheapest airline to Europe right now, and they fly out of there. And they're flying brand new Boeing 787 Dreamlines.
We're flying them tomorrow night to London and connecting with their flight into Rome.

David, it looks like NAS does not offer open jaw flights. I can only select one way or round trip on its official website.

What do you think of Kayak? I found every bit of information about each flight including flight duration, layover time, and plane type. A one-stop flight out of JAX would cost $1380 right now if I booked it on Kayak, but everyone says the airline websites are better due to inventory and price changes. That much information is not available on Delta.com so it is a good thing I checked a third party website!

NAS does not offer open-jaw. But since it does one-way flights at 1/2 the price of round-trips (effectively, since the surcharges for airport use mean that the two legs are often not the same price you can use NAS to book the various separate legs (or use a different carrier in the middle)

www.itasoftware.com will lead you to the matrix mentioned above. No search site covers every alternative but this one comes the closest, I think. It is owned by Google and serves the airlines, not consumers, so you can't buy tickets but you can see where to go. Unless your itinerary will combine airlines which do not sell each other's fares, airline sites are usually as cheap or cheaper than any other source and can make seat selection easier.

If you use a third-party vendor and you have a problem, you will have to have that vendor resolve it - the airline at whose desk you will probably be standing will not intervene, since they did not sell you the ticket.

I use Delta.com for almost all my flights, have found all the information I need on their website or through a phone call.

Mrs, the travel agent went on vacation. She will be back May 2. Mom plans to schedule an appointment for that date.

How do the alerts work on Sky Scanner?

I've never been able to see multi-city flights on Skyscanner, only one way or round trips. If there's a way, please share it.

http://www.momondo.com gives you both Multiple Destinations (aka. Open Jaw) and "Fare Alert" :-)