Before and during World War II, the Soviet Union conquered territories from Romania, Czechoslovakia, Finland, and annexed the Baltics and invaded Poland, the latter two being things that the Nazis did as well. So my question is, why we're they allowed to get away with this. What could've convinced the West to take a more hard line stance towards Stalin and Russia? And would Stalin give the conquered territories up if he was threatened with war?
Well, first, "allowed".
"Allowed" by whom? There was no body with the formal authority to forbid or allow the Soviet annexations. Neither the U.S. nor the U.K. nor both together had such authority, either.
By 1945, the USSR had acquired enormous credit for its fight against Nazi Germany. Even before that, a lot of left-wing intellectuals viewed the USSR through "rose-colored glasses", and the positive image of the USSR promoted for "Allied solidarity" during the war had affected even top political figures. FDR and many of his senior aides were profoundly naive about the USSR. No one had made the detailed critical studies that later revealed the enormity of Soviet crimes.
Instead there was a big gush of hopeful sentimentality about the UN and world peace.
So there was no will to challenge the Soviet annexations. Furthermore, they could all (more or less) be justified on historical grounds.
Moldova had been Russian territory before WW I, and its annexation by Romania had not been recognized by the western Great Powers (or so I have been told). Also, Romania had agreed to the cession in 1940, and then had become a German ally and joined in German crimes - so no one much cared about their territory.
The pre-war eastern border of Poland had no historical basis, being the result of the Soviet-Polish war of 1919-1922. Eastern Poland was Ukrainian and Belarussian speaking. The British government had tried to resolve the Soviet-Polish war by setting the border at the "Curzon Line" between Polish-speaking land and Ukraine/Belarus. So the annexation of those lands to the USSR was "justifiable", especially since Poland was to be "compensated" with German territory. And no one was going to object to any territorial losses by Germany.
The Baltic states had been Russian territory before WW I, and had peacefully submitted to the USSR in 1940. They were small, obscure places. The details of their fate seemed insignificant compared to the grand theme of World Peace through the UN, if the USSR cooperated.
Finland: those who remembered the Winter War could see what was wrong with Soviet actions. However, Finland
had ceded the border areas in 1940, had joined the Axis in 1941, and then had confirmed the border cessions in 1944. So by 1945 the cessions were already old news.
Ruthenia (the eastern end of Czechoslovakia): Czechoslovakia was only formed in 1918. Ukrainian-speaking Ruthenia was added only after some pulling and hauling with local nationalists, Ukrainian nationalists, and post-Habsburg Hungary. It had been annexed by Hungary in 1938. Czechoslovakia, newly restored, agreed to the cession to the USSR in 1945. Though obviously Czechoslovakia was effectively dominated by the USSR, they didn't fight at the time, so who else was going to? (And they didn't actually care that much; the Ruthenians had been an annoying ethnic minority.)
Basically, all these circumstances obscured the Soviet conquests. Western leaders and publics weren't seeing the USSR realistically.
And the Soviets had overwhelming power to enforce their conquests, unless the Western nations launched an all-out war. Britain was exhausted, bankrupt, and still fairly busy in India and the Middle East. The U.S. was demobilizing after the enormous effort of WW II. France was recovering from conquest and liberation, establishing a new constitution, and trying to avoid Communist takeover itself.
Bear in mind that as late as 1948, American left-wingers bitterly attacked Truman for "anti-Soviet warmongering", and Henry Wallace's protest candidacy drew over a million votes (about 2%).