The USSR did not occupy Romania and Hungary without a fight. You are looking for the "Jassy–Kishinev Offensive" and the "Budapest Offensive".

The Jassy-Kishinev offensive was an encirclement of German and Romanian forces in Romania. This resulted in hundreds of thousands of soldiers killed, wounded, or captured (mostly captured). It coincided with a coup in Romania (search term: "King Michael's Coup") which ousted the pro-Axis government and installed a pro-Allies government. Thus the remaining Romanian forces switched sides and started fighting Hungarians or simply surrendered and were deported to POW camps. It was quite obvious which way the wind was blowing in the fourth quarter of 1944 when the Soviets had basically recaptured everything they lost in Barbarossa and were showing no signs of slowing down. The USSR had taken very heavy losses, yes, but they were clearly winning, and the Germans were bleeding horribly too.

The army having laid down their arms and the Soviets already deep inside Romanian territory, the USSR was in control of the country. Yes, it's true that they could have continued fighting alongside the other Axis forces, but they did not.

The Budapest Offensive was basically the Red Army continuing to march North and West after the capitulation of the of the Romanians. They broke through Axis forces and seiged the capitol. The Hungarians, as the Romanians, did fight. However, after the official capitulation of the government, the Hungarian army did not lay down their arms as a whole unit, and did continue to fight alongside the Germans, some units even retreating out of Hungary and into the Reich once Hungarian territory had been completely overrun.

It is important to realize that WWII was as much a war of competing industries as it was a war of brave men armed with guns. The bravest platoon is of marginal worth against a katyusha rocket strike, a King Tiger or T-34s. In base military terms, neither the Hungarian nor Romanian militaries hosted enough high-technology weaponry to make a meaningful dent against Soviet offensives. Even in the late war, the Balkan nations' antitank weaponry was poorer as those of the German infantry battalions that had often faced a hard fight against the T-34 in 1941. Where the Germans had divisional artillery, the Luftwaffe and a very well-trained general staff, their Balkan allies had none of those.

It is in their failure to equip their allies that we see the true weakness of the German war machine. It is in their failure to understand their allies' deficiencies that we see another weakness in the Nazi racist ideology. While they might've had enough Panzer IVs and other models for their own soldiers, the Nazis did not have enough steel to effectively equip their allies. Contemporaries often saw the failure of Italians, Hungarians, Romanians or Poles in World War II to be a sign of racial degeneracy. Modern observers are more inclined to credit weapon systems. The Balkan nations looted and borrowed what they could. They used German and Italian planes. The Hungarians adopted the Turan tank from Czechoslovakia, but it was produced in the mere hundred. The Romanians imported the Panzer 38(t) from the same source. Neither tank was capable of outfighting the T-34, let alone the heavier tanks of the Soviet arsenal. The result of being far less well-armed than their unforgiving German allies resulted in massive demoralization amongst Hungarian, Italian and especially Romanian infantry forces (sources: Glantz, Beevor).

Unlike the Germans and Soviets, neither Balkan nation could replace their earlier war losses. While it is true that the Soviet Union had suffered immense wartime losses throughout the preceding years, it is not true that Hungary, Romania, or Germany had escaped lightly either. Hundreds of thousands of Romania's best-trained soldiers were encircled in the Stalingrad offensive, while Hungary's Second Army were basically wiped out in Operation Little Saturn. Of course, the Soviets lost millions of men in the Ostfront, but as the book 'Stalin's Keys to Victory' explains, the ability to replace lost armies was the true war-winning trait of the Stalinist system. Due to a comparatively stronger, more advanced economy, massive lend lease aid from America, and the motivation that comes from genocidal war and totalitarian propaganda, the Soviet Union was able to mobilize a much deeper conscription pool than either Romania or Hungary, the former of which struck even Soviet invaders as a poor land. More Romanian and Hungarian men were needed on the farms, making them unavailable as soldiers. What use is a soldier anyway, when you do not have the industrial base to arm, equip and supply them?

None of the aforementioned nations gave up without a fight. Their was deep fear and revulsion against Stalinism throughout Central Europe, and thousands of men were motivated to fight and die against the Red Army. They mostly died or surrendered. In the Jassy-Kishinev offensive, a very large military force of German and Romanian forces were outfought and encircled by their mobile Soviet opponents. Contrary to popular belief moreover, the Soviet front in southern Ukraine did not outnumber their Romanian-German opponents much in simple manpower. However, in airpower, artillery and tank equipment, the Soviets were miles ahead, and they effectively used that mobility to advance miles ahead of any fascist formations (source: Glantz).

After the collapse of Germany's Army Group South, there never was really any hope against the Soviets, though Hitler did order many SS formations to that front. Stalin now had the manpower pools of the USSR, Romania, Bulgaria, and Serbia to finish the war in the Balkans. Despite the power of SS King Tiger vanguards, new Soviet weaponry ranging from the Yak-9, IS-2, and ISU-122 shifted qualitative superiority away from the SS and Hungarians towards the Red Armies and their allies. In the approach to the Budapest offensive, hundreds of thousands of newly conscripted Hungarian troops were overwhelmed both in numbers by the Romanian and Soviet forces, as well as qualitatively by superior Soviet airpower, artillery and self-propelled tank weaponry. The Soviets were bruised by the long war, but they were willing and able to fight on.