At what time were the soviet's their most powerful in terms of military might and why?
Questions of comparative strength are extremely difficult to give you. They had more men under arms during the Second World War than later, but after 1949 they had atomic weapons, and after 1953 they had hydrogen bombs. ICBMs followed after Sputnik in 1957.
There's an argument to be made that the Soviet Union's ability to project power, relative to the rest of the world, has never been greater than in 1957.
For the purposes of your inquiry, are you referring only to conventional forces?