I have heard people describe the strengthening of USD in the 1980s as a direct attack on Soviet finances, but some of the people taking this view appear to have taken a rather conspiratorial approach to the whole situation to begin with.
As a small side request, I feel as if I once heard Yanis Varoufakis give his opinion on the matter and would be interested if anyone knew where I might find this (I thought it was in a talk he gave with Stiglitz but apparently not).
The strengthening of the USD isn't so much because of the Soviet Union, it's because of spiraling inflation in the 1970s. Inflation, which had peaked at around 13.5% per annuam was seriously destabilizing to the American economy. The need to curb inflation was recognized as necessary. The Federal Reserve under Paul Volker was determined to bring down inflation, and thus strengthening the dollar by definition.
Oil prices dropped largely because of excess supply, induced by high prices in the 1970s, oil producer were incentive to overproduce. This was epecially an issue because in 1979-1980 already high oil prices once again doubled from already very high prices. Producers flooded the market trying to make more money from the higher prices, but that naturally drove down prices on the long run and thus causing the 1980s oil glut.