I don't think Italy would have remained neutral throughout the war, my guess is Mussolini would have waited until around 1944 to join the allies and made it a condition that Italy would be a permanent member of the UN security council with a veto. Also, I wouldn't rule out Italy becoming a nuclear power by the 1950s. These two things would have cemented Italy's "great power" status in the post-war world.
With this turn of events, Italy could have easily controlled its empire indefinitely. Portugal was able to hang on to its empire until 1975, so Italy with 6 times as many people and an economy 9 times larger than Portugal's could have easily held on to theirs longer. Also, Portugal had to cope with an arms embargo that limited the equipment they could use in their colonies. Italy on the other hand is a major arms producer with the ability to field a much larger army.
To defend itself, Italy would have been drawn to an alliance with France in the 1950s as Italy would try to keep Algeria and especially Djibouti from falling into hostile hands. I'd imagine with fascism being seen as distinct from Nazism that DeGaulle and Mussolini could see themselves as the "third force" leading an alternate bloc of countries. I can see this bloc including Portugal, Spain, Argentina, Brazil and possibly Turkey or Bulgaria (if they manage to stay out of the war).
Israel would be another important ally, especially after 1956. If Italy keeps Libya, they'd incur the wrath of the Arab countries, making the two countries natural allies. Perhaps with a staunch ally on the security council there would be no pressure for Israel to make peace with Egypt and to keep the Sinai. Unlike the United States, Italy would make have no qualms of offending the Arab bloc. The two countries can share technology and intelligence and keep Egypt in check.
Another set of allies would be the ideologically similar Portugal as well as South Africa and to a lesser extent post-UDI Rhodesia. This would have repercussions on Africa as Italy would be able to openly sell arms to these countries without worrying about UN sanctions and not caring about the opinion of the Afro-Asian bloc. This would especially be invaluable to Portugal which in OTL in 1939 had allowed the Italians to build an airport in Cape Verde, perhaps for more direct assistance they would have allowed the Italians to have an airbase there.
Here's an analysis of the Italian colonies:
Libya was already considered an integral part of Italy and in 1940 the Italians accounted for 12% of the population. Even though mass settlement schemes had only begun in 1938, Libya had the same percentage of settlers as French Algeria after over a century of French rule. Mussolini's plans were much more ambitious and by 1960 there were to be 500,000 agricultural settlers in Libya. Italians were already a slight majority in the cities and with the discovery of oil there would be many more Italian settlers pouring into the Tripoli and Benghazi. The Italian population would have likely exceeded the Arab population by the early 1970s and I'd imagine that poor Libyans would start to migrate to Northern Italy, just as the Arab Algerians had done starting in the 1950s. Th Arab population would be much lower since in OTL Libya has relied heavily on immigration from other Arab countries to boost their population, I'd imagine the Italians would shy away from importing more Arabs into the colony.
Italian East Africa would have been a bigger challenge to keep. Maintaing this huge colony rests on keeping the Suez canal open, and expect Italy to take part in the Suez campaign of 1956. Also, I'd imagine Nasser's Egypt would be hostile to the Italians and harbour any Libyan rebels. This would probably draw Italy and Israel into an alliance. Also, to keep air routes open, I'd imagine Italy would try to setup a puppet government in Sudan after 1955 or actively support the Southern Sudanese in their civil war against the North.
Mussolini had huge plans for East Africa, and was able to send encourage the settlement of 190,000 Italians in 5 short years. In contrast, Southern Rhodesia would only achieve that number of settlers in 1957 after 67 years of British rule. Eritrea had some 90,000 Italian settlers alone and Asmara had a European majority (by comparison at their peak whites only were 12% of Nairobi's population). I'd imagine that by 1960 there would be over 1 million Italians in the territory, a large enough minority that they'd demand that Italy protect them from majority rule. This would inevitably lead to a protracted guerilla war, with the insurgents being supplied by the Soviet Union and China with and possibly using Kenya as a base.
Albania was mentioned earlier, and I'd imagine that this would be the toughest place to subdue. With its mountainous terrain it could have been very difficult for the Italians to keep hold of. I'd like to think that in this timeline Mussolini has some sort of sanity around 1937 or 1938 and doesn't bother annexing Albania. King Zog's Albania was already friendly to the Italians and would have been much better as an ally than as a occupied protectorate. The Dodecanese Islands would inevitably caused some friction with Greece which is why I see the Italians being friendly with Turkey, Bulgaria and an unoccupied Albania instead.
Finally, I could imagine Italy would act a bit like a great power if attacked. Meaning that if Kenya or Sudan sought to supply pro-independence movements that they'd have to deal with air strikes. In OTL Tanzania's Julius Nyrere was a major backer of the southern African liberation movements and Tanzania could become a target for Italian reprisals. Jomo Kenyatta would probably be a bit more pragmatic and not want to be too brash with the Italians.
With this turn of events, Italy could have easily controlled its empire indefinitely. Portugal was able to hang on to its empire until 1975, so Italy with 6 times as many people and an economy 9 times larger than Portugal's could have easily held on to theirs longer. Also, Portugal had to cope with an arms embargo that limited the equipment they could use in their colonies. Italy on the other hand is a major arms producer with the ability to field a much larger army.
To defend itself, Italy would have been drawn to an alliance with France in the 1950s as Italy would try to keep Algeria and especially Djibouti from falling into hostile hands. I'd imagine with fascism being seen as distinct from Nazism that DeGaulle and Mussolini could see themselves as the "third force" leading an alternate bloc of countries. I can see this bloc including Portugal, Spain, Argentina, Brazil and possibly Turkey or Bulgaria (if they manage to stay out of the war).
Israel would be another important ally, especially after 1956. If Italy keeps Libya, they'd incur the wrath of the Arab countries, making the two countries natural allies. Perhaps with a staunch ally on the security council there would be no pressure for Israel to make peace with Egypt and to keep the Sinai. Unlike the United States, Italy would make have no qualms of offending the Arab bloc. The two countries can share technology and intelligence and keep Egypt in check.
Another set of allies would be the ideologically similar Portugal as well as South Africa and to a lesser extent post-UDI Rhodesia. This would have repercussions on Africa as Italy would be able to openly sell arms to these countries without worrying about UN sanctions and not caring about the opinion of the Afro-Asian bloc. This would especially be invaluable to Portugal which in OTL in 1939 had allowed the Italians to build an airport in Cape Verde, perhaps for more direct assistance they would have allowed the Italians to have an airbase there.
Here's an analysis of the Italian colonies:
Libya was already considered an integral part of Italy and in 1940 the Italians accounted for 12% of the population. Even though mass settlement schemes had only begun in 1938, Libya had the same percentage of settlers as French Algeria after over a century of French rule. Mussolini's plans were much more ambitious and by 1960 there were to be 500,000 agricultural settlers in Libya. Italians were already a slight majority in the cities and with the discovery of oil there would be many more Italian settlers pouring into the Tripoli and Benghazi. The Italian population would have likely exceeded the Arab population by the early 1970s and I'd imagine that poor Libyans would start to migrate to Northern Italy, just as the Arab Algerians had done starting in the 1950s. Th Arab population would be much lower since in OTL Libya has relied heavily on immigration from other Arab countries to boost their population, I'd imagine the Italians would shy away from importing more Arabs into the colony.
Italian East Africa would have been a bigger challenge to keep. Maintaing this huge colony rests on keeping the Suez canal open, and expect Italy to take part in the Suez campaign of 1956. Also, I'd imagine Nasser's Egypt would be hostile to the Italians and harbour any Libyan rebels. This would probably draw Italy and Israel into an alliance. Also, to keep air routes open, I'd imagine Italy would try to setup a puppet government in Sudan after 1955 or actively support the Southern Sudanese in their civil war against the North.
Mussolini had huge plans for East Africa, and was able to send encourage the settlement of 190,000 Italians in 5 short years. In contrast, Southern Rhodesia would only achieve that number of settlers in 1957 after 67 years of British rule. Eritrea had some 90,000 Italian settlers alone and Asmara had a European majority (by comparison at their peak whites only were 12% of Nairobi's population). I'd imagine that by 1960 there would be over 1 million Italians in the territory, a large enough minority that they'd demand that Italy protect them from majority rule. This would inevitably lead to a protracted guerilla war, with the insurgents being supplied by the Soviet Union and China with and possibly using Kenya as a base.
Albania was mentioned earlier, and I'd imagine that this would be the toughest place to subdue. With its mountainous terrain it could have been very difficult for the Italians to keep hold of. I'd like to think that in this timeline Mussolini has some sort of sanity around 1937 or 1938 and doesn't bother annexing Albania. King Zog's Albania was already friendly to the Italians and would have been much better as an ally than as a occupied protectorate. The Dodecanese Islands would inevitably caused some friction with Greece which is why I see the Italians being friendly with Turkey, Bulgaria and an unoccupied Albania instead.
Finally, I could imagine Italy would act a bit like a great power if attacked. Meaning that if Kenya or Sudan sought to supply pro-independence movements that they'd have to deal with air strikes. In OTL Tanzania's Julius Nyrere was a major backer of the southern African liberation movements and Tanzania could become a target for Italian reprisals. Jomo Kenyatta would probably be a bit more pragmatic and not want to be too brash with the Italians.