Extremely disruptive. In general, the GDP of a country declined by around 33-50% on average after major fighting began in the country, as shown by historical GDP figures compiled by Angus Maddison. This significant decline represented a sharp decline in the standard of living. As for who expreienced extremely poverty, this is more difficult to answer because poverty is a relative standard set by different organizations and governments to begin with. Further, it is typically defined in monetary terms, which is largely fruitless in a wartime economy because rationing severely limits the buying power of money. It would not be an exaggeration to say the majority of Europeans and East Asians by January 1945 were living in a state analogous to modern poverty from a standard of living perspective, as by then Germany, the USSR, and Japan had all transitioned to full economic mobilization in their own countries and in countries they had occupied. Consumer goods were increasingly rare, even for people with plenty of money. However, this is not reflected in monetary realities.
From the standpoint of goods-scarcity, the war in total displaced around 60 million people, leaving them wihtout housing. Responses to this varied. In the Soviet Union, evacuated populations, consisting of upwards of 16.5 million people, were moved into scant state-provideed shelters or were quartered with residents in the country's interior. In Japan, victims of homelessness due to bombing typically lived with relatives or created makeshift shelters amid the rubble. Perhaps surprisingly, Cormac Grada contends that the USSR was the only major power during the war to experience famine. Minor countries also experienced famine, with upwards of 200,000 Greeks dying in famine between 1941 and 1942, and the Netherlands in 1944 and 1945. Despite the relative rarity of famine, food shortages were acute and almost universal. While German and British rations on the home front were, for most of the war, adequate, German rations in occupied countries left the population either reliant on extra food from the black market or constantly verging on the brink of starvation. One report from 1942 states:
At the end of 1940 Polish rations of fats amounted to only 25 per cent of the German ration; sugar and meat, 50 per cent; and bread, 75 per cent of the German allotment. In Czechoslovakia, the wheat ration was about 50 per cent of the German allowance. Rations in Holland, Denmark and Norway were said to be about equal to those in Germany. The same source stated that Belgium had the smallest bread and sugar ration of any of the western occupied countries.
This policy made an inadequate diet not only universal, but enforced in all German-occupied countries except those favored by Germany - namely Holland, Denmark, and Norway - and France, which had a measure of independence.
Altogether, concrete numbers for the "poverty rate" of wartime Europe and Asia are impossible to come by. However, from the standpoint of goods scarcity, well near the majority of the European population was living in conditons analogous to modern poverty, including a lack of housing and an inadequate diet.
Sources:
Maddison, Angus. Maddison historical statistics.
Kesternich et al. The Effects of World War II on Economic and Health Outcomes across Europe.
Lee, Kendrick. Wartime rationing.
Wheatcroft, Stephen and O Grada. The famines of World Wars I and II.