One tool to get a sense of the diversity in Italy is to look at the languages spoken there during the iron age. Even if language does not always map to ethnic identity, it's still a useful tool. To name a few (I am taking this mostly from Mallory):
Ligurian (Ligures, IE, possibly Celtic)
Lepontic (IE, Celtic)
Etruscan (Tyrsenian, non-IE)
Raetic (also thought to be Tyrsenian and related to Etruscan)
Umbrian (Umbri, related to Oscan)
Oscan (Sabines, Aurunci, Sidicini, Ausones)
Massapic (Iapyges, Dauni, Peucetii; possibly related to Illyrian)
N. Picene (undeciphered)
S. Picene (probably IE)
Venetic (IE, centum language, classification debatable)
Latin (closely related to Faliscan)
Faliscan (Falisci, closely related to Latin)
What this suggests is two things:
1. The presence of a neolithic Tyrsenian substrate; of course how extensive or homogeneous this was remains unknown. There could have been multiple non-IE peoples on the peninsula long before the arrival of the first Indo-Europeans. It would be interesting to know what hg(s) correspond to the Tyrsenians.
2. What looks like multiple waves of Indo-European diffusion, similar to what happened in Greece, and quite a lot of diversity even within the IE languages on the peninsula.
And of course this leaves out Sicily and all the later influences (Greek, Punic, Arab, Norman, Lombard, etc.)
As to number 1: There is quite a bit of evidence that the Neolithic that arrived in the south, from the area of Albania, for example, was different from that in the north, with the northern Italian Neolithic still retaining some interest in supplementing their diet with hunting, which the Neolithics in southern Italy by and large were not doing. That might indicate slightly different streams of the Neolithic, although of course, the south might have been over-hunted as well.
I would agree with number 2.
As for number 3,the Greek impact is clear. However, in my opinion, any Phoenician or Carthaginian impact would have been minor. The Phoenicians were traders who set up emporia; I'm not aware of any proof that they set up any colonies in Italy that would have included substantial numbers of colonists, unlike the Greeks for instance. There is a study of southern France that proves that point and might apply to Italy for comparison purposes.
The Normans were a very small group of men, mercenaries really. As members of an elite, (a mixed Scandinavian/Gallic group) they might indeed have left traces in the y dna, but autosomally, their contribution would basically have vanished, in my opinion. Btw, the area in France where the "Vikings" settled, while it does have some U-152, is higher, I think, in L-21, which hasn't shown up in northwestern Sicily to my recollection. That isn't altogether surprising, as the "Normans" were formed by a combination of Scandinavian men and French women. Some local men, Bretons, for example, certainly formed the contingent that went to England, but perhaps there weren't that many of them among the group that went to Sicily. I'll check my books.
The "Lombards" who were, to be precise, northern Italians from Lombardia, Piemonte, Liguria and other northern Italian areas, do represent a "folk" movement of peoples, a movement which has had the greatest impact, in my opinion, on the Sicilian genome in more recent times. Whole towns in the interior were established for them, towns which had been depopulated of Muslim Sicilians.
The "Arabs" didn't invade Sicily. They were Berbers, initially mainly from nearby Tunisia, although as in any invasions of this type you had adventurers from other areas of the Muslim world. Their presence can be traced most easily via the E-M81 clade, I believe, and perhaps the North African clade of J1 as a minority component, and it is surprising small considering all that has been written and said about the "Moorish" influence on Sicily. One could also, of course, add in some of the other clades of "E", although not E-V13, and even with some of the other "E" clades, you would have to get down to the sub-clade level and date the subclades to get a handle on whether they fit the time period, or are just as likely to have come with the Neolithic or the Bronze Age. Another thing that has to be taken into consideration is that the Normans and later Frederick II, did their own version of ethnic cleansing in Sicily. As with other such claims, I doubt it was as complete as they claimed, but that it happened is irrefutable.
There is a wonderful book about this whole period called A History of Muslim Sicily, by Leonard C. Chiarelli. In it, there is a poem by an exiled Muslim Sicilian:
"My hands are empty, but my eyes are filled with your memories, Sicily".
I highly recommend the book.
Ed. The "Moorish" invaders of Sicily were *mostly* so far as can be determined, North African Berbers, although there were definitely Arabs amongst them; in fact, some of the power struggles on the island can be traced to differences between these two groups.