The sagas tell of expeditions to many places,
among them it's told of a group that took up hire as troops for a Greek King.
It's also been found a grave and a rune stone telling of an expedition to the holy land, but this was in late Viking era and we don't know what they were doing there, only that the chieftain died there, not in battle, (they were quite specific about dying in battle or not) but if it was sickness is unknown.
What's clear is that at least some of the crew managed to get back home.
I thought the Roman Empire ended in several "Italian" city states eventually,
but I'm not sure when that began, just that I think that during the 1500s at least there was some fighting between city states, and such.
Creating a need for mercenary outfits, similar to the Landsknechts of Prussia.
And that by the late 1500s these armies were so well equipped with armor and swords, and that since they only worked for money, fights between them turned into much dueling on the battlefield and the aim to capture your enemy so that you could sell him back to his Merc leader "captain", who after all would rather pay to get experiences troops back than paying salary and training for new ones. But while I've heard that many such smaller skirmishes happened, there was also some brutal sieges now and then.
Also these professional armies proved very effective and brutal when fighting invaders from other nations.
But I have no doubt many northerners have lineage in Italy, as all of Scandinavia are sea faring nations.
From the Viking era and up, (and also in some lesser degree even earlier)
sailors have settled all over the world.
Some places more than others.
In France the Normans were of Viking descent, and it's ironic that William the Conqueror defeated the English King Harold, who had just won the battle of Stamford bridge against Harald Hardrade (litteralt Harald hard/stern-ruler) in 1066. The Norse kings following managed to stay on friendly terms with William, but England was no longer a country to plunder, or as in the 900s, they usually just asked for bribes not to attack.
(One also has to remember that Harold, an anglosaxon, was a descendant of Canute (Knut) the Great, who had been King of Denmark, Norway and England in the beginning of 1000AD.
Canute inherited the Danish throne, and his troops supported and claimed him King of England.
So he took England with help from the Norwegian King Olaf the Holy (Olav Trygvasson) in 1016.
Later Olaf the Holy turned against Canute, and formed allegiance with the Svea/Swedish Anund and earl Ulf.
Canute sent 1400 longboats to Norway, won over Olafs and his allies armies, and became its King in 1026. Later that year Earl Ulf was murdered in a church.
Drifted off here. Tired but love history.
Just ranting about history.