Well, for Ethiopia we need to remember 2 things.

1. After the Italian occupation of Ethiopia in 1936, Emperor Haile Selassie lived in exile in England from 1936-1941.

2. the East African campaign in 1940-1941 saw Italian forces invade British Somaliland, and subsequently colonial forces from British Sudan, Kenya, South Africa, Belgian Congo, and Ethiopian freedom fighters drive Italian forces out of East Africa by 1941.

Emperor Haile Selassie was deeply involved in the East African campaign, particularly in the role of making speeches and rallying Ethiopian resistance and insurgency against Italian occupation. By May of 1941 he had crossed from Anglo-Egyptian Sudan into Ethiopian territory and proclaimed his restoration, with the support of the British. By November of 1941, Italian forces had been effectively defeated (although Italian insurgency would linger on in the countryside into 1943).

So, the answer to the Ethiopian part of your question is that by the end of WWII, Ethiopia had been restored to independence for some 4 years, under the rule of Haile Selassie.

Of course, there were some questions about how Italian colonies in the Horn of Africa (Eritrea and Italian Somaliland) should be administered after WWII. Eritrea had been administered under British military government from the Italian military defeat in 1941. A diplomatic resolution to the Eritrean question was not swiftly decided, and various proposals were floated from returning Eritrea to Italy as a UN trust territory; dividing it between Anglo-Egyptian Sudan and Ethiopia; or awarding it entirely to Ethiopia.

In the end, the British military government continued until 1950, when a UN resolution federated Eritrea with Ethiopia. (that is, Eritrea was expressly granted certain rights of self-governance, but her foreign affairs were to be governed by the Emperor of Ethiopia).

Italian Somaliland similarly was governed by a British military government from 1941-1949. But in this case, the territory became a UN Trust Territory under Italian administration. However, the resolution that established it as a Trust Territory had specific stipulations that Italy was only to administer Somaliland until 1960, at which point the territory would be granted independence. There were specific guidelines laid out stipulating how Italy must prepare Somaliland for independence. In April of 1960, the legislature of British Somaliland (a british protectorate) requested independence, which was granted in anticipation that the British Somaliland territory would unite/merge with the Somaliland Trust Territory to form one country. This merger happened on July 1, 1960, and the two territories formed the Somali Republic.

In terms of Libya, there was once again British military administration from 1943 through the end of the war. Additionally, Free French forces (later forces of the French 4th Republic) administered the southern Fezzan region which bordered French colonies of Algeria and Chad.

With the signing of a formal peace-treaty between Italy and the Allies in 1947, Italy renounced all claims to Libya. As with Eritrea and Somaliland, there was not an immediate diplomatic consensus to what the position of Libya should be, and British and French delegations attempted to secure the status quo by seeking UN approval for making Tripolitania and Cyrenaica into British trust territories, and Fezzan into a French trust territory. However, these proposals were deeply unpopular both with Libyans, with American and Soviet diplomats, and with leaders in the Arab world. A UN resolution in 1948 passed in favor of Libyan independence, to take effect in 1951. Idris al-Senussi, the emir of the Senussi religious order which had fought a long war of resistance against Italian occupation from 1913-1922 was well placed politically to lead the new nation, and became the (first and only) king of the new Kingdom of Libya in 1951.