The Suez Crisis was not really about oil, although it was one of the goods that flowed through the Suez, and Middle-Eastern oil was an important part of the geostrategic importance of the region, which made it matter so much for the UK. But, if oil had been the UK's prime concern, they would have acted as forcefully as they did in Suez when the Iranians nationalised the Anglo-Persian Oil Company in 1951.

To understand the Crisis, you must first understand that the Suez Canal was owned by the British, and partially by the French, through their ownership of the Suez Canal Company. This meant that literally every good coming through the Canal, including the oil you mentioned, was money for the British and French governments. In addition to this, control of the Canal was a huge geostrategic boon, since it meant that the UK controlled the fastest route to Asia not only for itself, but for everyone else.

Especially for Britain in the mid-50s, the geostrategic aspect was even more important than the money from all the goods passing through the Canal. Since the loss of India and Pakistan, Britain's value in the Cold War, it's claim to continued World Power on par with the United States and USSR, had become increasingly tied to British influence and control in the Middle-East. The Anglo-Persian Oil Company had indeed been a part of this calculus, but not one that was considered absolutely integral.

The Canal Zone, however, most definitely was absolutely integral. Without the Canal, British leverage would be just a couple air bases and a Mediterranean Presence provided by Malta and Cyprus. Not to mention, the British empire had always operated on the international stage on Prestige as a fundamental foundation; the perception of the British was just as important as the actual empire. To lose Suez, a supposed superpower bowing down to a former colony, would be a massive blow to Britain's prestige. And the British government really did consider "The Third Superpower" as the UK's place in the world.

This was the environment for Britain in which Egyptian President Nasser nationalised the Canal, placing the Company under the control of the Egyptian Government. For the French, it was bad, for the Israelis, it was worrying (an Arab power gaining leverage), for Britain, it was absolutely catastrophic. Not only were the profits from the Canal Company under threat, but the entire underpinning of Britain's Superpower Status.

The invasion of the Canal, begun as an "unrelated" invasion of the Sinai by Israel, being a colonial power's invasion of a former colony trying to take back it's own land, was an absolute disaster diplomatically. It took away from the USSR's crushing of the Hungarians and strengthened their support in the Middle-East by painting the West in an imperialist light, and it temporarily harmed US-UK relations because the UK did not consult the US before it invaded. Eisenhower called Eden and gave him "a tongue-lashing that reduced the Prime Minister to tears." [1]

Most of all though, the UK's withdrawal upon the lack of American support absolutely crushed the final illusions of Britain's continued world power. Not only could they do nothing without American support and were thus in no way the Superpower they claimed to be, but the rhetoric they had espoused throughout the late '40s and early '50s, of a mutually co-operative, democratic, Commonwealth of Nations was exposed as empty; definitively a smokescreen for continued Empire in all but name. If there was any hope of Britain maintaining a similarly close relationship to its other colonies post-independence as it had with the White Dominions (Canada, Australia, New Zealand, South Africa), it was completely snuffed out by Suez.

The next decade would see the British Empire unravel quickly and completely. 12 years later, Britain's African possessions would all be independent and it would leave its bases East of Suez, having no military presence there for the first time since the 1700s. Suez is, with good reason, seen as the point where the British Empire went from struggling seriously to unconscious and bleeding out on the pavement.

As for Australia, it was at the time still much more integrated into the UK geopolitically. At least as far as Prime Minister Robert Menzies seemed concerned, there was really no distinction between the geostrategic concerns of the UK, and those of Australia. He even mentioned the notion of prestige:

"It is apparently not fashionable to speak of prestige. Yet the fact remains that world peace and the efficacy of the United Nations Charter alike require that the British Commonwealth and, in particular, its greatest and most experienced member, the United Kingdom, should retain power, prestige, and moral influence."

Menzies and the Australian Press were in some ways more hawkish than that of the UK, opposing any effort to consider the nationalisation of the Canal as legal. Once armed intervention began, Australia and New Zealand were in fact the only nations in addition to the triumvirate of the UK, France, and Israel, to oppose a UN Resolution to halt movement of arms and men to the Suez. Australia was also one of ten abstentions to the UN Resolution for withdrawal from the Suez (only Israel explicitly voted against). The press was more divided on armed action.

After the entire incident was over, Menzies continued to defend the British and French decision in Canberra.

[1] - Patterson, James T., Grand Expectations: The United States, 1945-1974, (Oxford, 1997) 307

TL;DR: For the UK especially, it was about pretty much everything other than oil. The entire underpinnings of the British Empire and Britain's world power were invested in the Middle-East, and thus the Suez Canal. The humiliating failure of the invasion stalling completely on a lack of American support destroyed the illusion of the British Empire and strengthened the USSR by painting America's allies in a bad light in the Middle-East. Australia was on Britain's side officially, but divided in the press once actual military action began.

Sources:

David Goldsworthy (ed.), The Conservative Government and the End of Empire 1951-1957, (London, 1994)

Ronald Hyam (ed.), The Labour Government and the End of Empire 1945-1951, (London, 1992)

Darwin, John, The Empire Project: The Rise and Fall of the British World-System 1830-1970, (Cambridge, 2010)

Darwin, John, Unfinished Empire: The Global Expansion of Britain, (London, 2013)

Kennedy, Paul, The Rise and Fall of the Great Powers, (New York, 2013)

W. McMahon Ball, 'The Australian Reaction to the Suez Crisis', Australian Journal of Politics and History, 2 (1957), 129-150