Italy and Japan were unopposed in their aggressions at the beginning of the war because the major powers, such as the United States, Great Britain, and the Soviet Union, were either not yet involved in the conflict or were preoccupied with their own issues.
Italy under the rule of Benito Mussolini sought to expand its territory through aggressive military action in North Africa and the Mediterranean. Italy's first major conquest was Ethiopia in 1935-1936, which was followed by the invasion of Albania in 1939. Despite protests from other nations, no country was willing or able to stop Italy's expansion until the outbreak of World War II.
Japan, under the rule of Emperor Hirohito and the military leadership, sought to establish dominance in East Asia and the Pacific. Japan's aggressive expansion began with the invasion of Manchuria in 1931 and continued with the invasion of China in 1937. Despite condemnation from other nations, Japan continued its aggressive expansion until it sparked the United States' entry into World War II with the surprise attack on Pearl Harbor in December 1941.
Overall, the major powers were preoccupied with their own concerns and did not take action to prevent Italy and Japan from expanding their territories through aggressive military action until the outbreak of World War II.