Why did the nazi use euphemisms like "final solution" and resettlement? how did it assist them in their efforts?

The Nazis used euphemisms because it would make their monstrosities seem less like monstrosities. This is a common strategy in politics and some countries and politicians go as far as not only to use euphemisms, but use positive descriptions of actions which might be considered a crime against humanity.

present participle > C
infinitive > A
past participle> D
gerund > B