The Japanese did not actually lose many of the oil fields of the Dutch East Indies during WWII. At the end of the war, they were still in control of the islands of Java and Sumatra, while Borneo had only been invaded in May 1945. They had, however, lost control of the sea lanes running from the oil fields to the Japanese home islands. The American submarine campaign had sunk many of the Japanese tankers, while the fall of the Philippines and Okinawa had allowed surface ships and aircraft to maraud across them. In addition, the Allies ran several carrier raids against the oil fields and refineries. Some strategic bombing attacks were carried out, mainly from Australia and Papua New Guinea.
While these attacks were mostly successful in reducing the flow of oil from the Dutch East Indies to a mere trickle, they did not completely cut off Japan from oil. Japan had several domestic oil fields, on Honshu and Hokkaido. These produced over 700,000 barrels of oil in the first half of 1945, most of which went to the aviation forces. They were also able to produce synthetic oil, from coal and oil shales. This was a highly effective means of production, producing 500,000 barrels in the four months between May and August 1945. Less conventional means of production were also explored. Pine roots were dug up, as the oil they contained could be distilled to obtain a usable form of aviation fuel.
The navy suffered most from the lack of oil. In June 1944, they salvaged 580 tons of fuel oil from the wreck of the battleship Mutsu, which had sank in the Harashijima anchorage after an accidental explosion. The task force sent to Okinawa as part of Operation Ten-Go, which included the Yamato, had only enough fuel for a one-way trip. Many of the IJN's surviving warships would end the war at anchor in various harbours, with only just enough fuel for a single one-way trip to the site of any landing.
Sources:
Nemesis: The Battle for Japan, 1944-45, Max Hastings, Harper, 2008
Rising Sun: The Decline and Fall of the Japanese Empire 1936-1945, John Toland, Pen and Sword Military, 2005
Oil Fields and Refineries Under Japanese Control, Bob Hackett, combinedfleet.com, 2014
Oil was one of the crucial bottlenecks of Japan's war effort and the latter third of the war was marked by an increasingly desperate efforts to mitigate Japan's lack of oil.
The dilemma for Japan was that its main sources of oil in Borneo and the Netherlands East Indies were both geographically distant from the home islands and only barely produced enough oil to meet Japan's war effort. The problem of distance became increasingly acute around mid-1943 as the US submarine blockade tightened and Japan's tanker fleet was inadequate for the task at hand. Japan had some 300,000 ton tanker capacity at the start of the war, but that was only just adequate for Japan's needs. New tanker construction could not make good the losses from submarines and mines. The Japanese resolved this dilemma somewhat by rebasing a good portion of their fleet, one of the largest consumers of oil, closer to the oil reserves in SE Asia in 1944. The anchorage of Tawi-Tawi became one of the main bases of the Combined Fleet in mid-44 as its proximity to Tarakan's oil fields overshadowed its many deficiencies as an anchorage.
Yet relocation of the fleet did not resolve the issue of oil in the Home Islands. The Japanese expanded whatever domestic fields they possessed and tried to husband whatever oil came through the Allied submarine blockade. Domestic oil production expanded in Hokkaido and the western coast of Honshu, but poor Japanese extraction technology limited these efforts. Japanese drilling was inefficient and seldom repressurized the wells after use, which put a ceiling on their further expansion. From 1942-44, Japanese domestic annual oil production consistently hovered at around 1.5 million barrels. The occupation of the Philippines in late 1944/ early 1945 cut off much of this tenuous supply line by extending Allied airpower's ability to interdict seaborne trade. The Japanese bandied about with desperate measures. One measure was the Ki-105 Otori, a powered-modification of the Kokusai Ku-7 glider. The Ki-105 would be an airborne tanker that could carry a marginal amount of fuel back to the Home Islands. Because of the distances involved, the aircraft would use up to 80% of its initial payload in the return leg. The I-351 class submarine was a more conventional approach to blockade, but this was just a sop to Japan's fuel needs.
In addition to these measures, the Japanese responded to the blockade with ersatz oil. The Japanese synthetic fuel program received new attention from the government in mid-1943, but produced meager results. The Japanese built plants to derive oil from coal and shale in the Home Islands and Manchuria. The Japanese made a choice in 1942 to deprioritize synthetic production in favor of shipbuilding, aircraft construction, and other aspects of wartime heavy industry on the assumption that their SE Asia sources were secure. The largest plant, the Fushan Works of the Manshu Synthetic Oil Company in Manchuria produced some 55% of Japan's total production, a telling indices of how paltry this output was compared to Japan's needs. Although synthetic oil produced a fair degree of production, its output was far short of the quotas set out by the Japanese. USSBS surveys conducted after the war noted that in 1943, the Japanese economic planning forecast some 14,460,000 barrels of synthetic fuel, the industry only produced 1,048,000 barrels. Synthetic oil production peaked in 1944, averaging around 100,000 barrels a month, but 1945's averages were at half of that level.
The Japanese began to experiment with various substitutes for petroleum, such as oil derived from pine roots, sweet potatoes, and soybeans. The latter was particularly tempting as Japan was not yet quite cut off from Manchuria and Korea. However these alternative fuels were decidedly poor in quality and the aircraft engines suffered a marked decline in performance.
So to answer the OP's question in a roundabout way, the Japanese tried various measures escape their oil bottleneck that yielded results ranging from inadequate to catastrophic. These failures meant that the Japanese war effort increasingly started to reemphasize fighting without oil. This meant a conversion of powerplants on land and at sea to coal. Trains and other civilian transport was curtailed and moved over to charcoal and wood gas. Ships that were incapable of being reconverted were simply laid up and their AA suite supplemented harbor defenses. IJA motorization, never that strong to begin with, became deemphasized. The few reserves of aviation fuel left were husbanded for final attacks and the training regime of Japanese fliers became increasingly ground-based link-trainers. The paucity of oil became another component underlying the increasingly desperate nature of Japan's war effort in 1945.
Edit: tweaked with some specifics
Sources
Evans, David C., and Mark R. Peattie. Kaigun: Strategy, Tactics, and Technology in the Imperial Japanese Navy, 1887-1941. Annapolis, Md: Naval Institute Press, 1997.
United States Strategic Bombing Survey. Oil in Japan's War. Washington, D.C.: Oil and Chemical Division, 1946.