The best way to search flights comprehensively is at oldmatrix.itasoftware.com.
You can put in any number of origins or destinations.
For your example, I'd navigate to that site and search 1 way.
From: LAS
To: FCO, ATH
And select the month long search around your dates, which will give you a calendar showing the cheapest price for each day of the month to either place.
If you wanted to expand the trip you can add any number of places.
For example
From: LAD
To: FCO, VCE, NCE, BGY, MXP, ATH, VIE
If you don't know the airport codes it will supply a list of airports within various distances of up to 500 miles from your original choice if you click "nearby".
Then do the opposite search for the way home.
You mentioned airline preferences, and you can filter your search by airline or airline alliance as well, either before searching or in your results, and also can limit your number of stops, total travel time, etc. It's infinitely flexible.
In terms of airlines, it's very likely the cheapest route from Las Vegas to Rome will be on Westjet Airlines connecting in Calgary, Canada. I did the search mentioned above for July and it was more than $400 USD cheaper per person than any other option. Downside is you have to clear Canadian immigration while connecting, but you're guaranteed a 787 Dreamliner no more than a few years old, and assuming you're going in spring/summer/fall for your cruise weather on the connection is unlikely to be an issue.
Edited to add: they don't sell tickets, but once you find exactly what you want you can search that specific thing on the specific airline site. It's better to buy tickets directly vs through an online travel agent in case of any issues.