When Ares increases his power, he boasts he is as strong as Hercules. That is the Roman name of the demigod while all other mythical figures in the film are identified by the proper Greek names of Greek mythology. Though technically the proper name of Heracles would have applied, the source material of the comics has a long of intermixing the names of Roman and Greek deities in The Pantheon.
Before Ares launches a nuclear missile at Themyscira he tells wonder woman that "you're being optimistic if you think I've reached the height of my powers. You see, since I've been gone, man has created a weapon of such awesome destructive force that the use of just one of these weapons feeds me with the psychic energy of 1,000 wars." Then he gets more powerful. This implies that the nuke reached Themyscira and killed thousands of people, but later you see that Steve Trevor destroyed the nuke before it hit Themyscira. Ares is able to draw power acts of violence. When he received strength from the "use of just one of these weapons" he meant that merely launching the nuke (which in itself is an act of war) gave Ares the aforementioned power. This is evident in that when Ares grows stronger, the nuke is seen taking off in the background.
On the island, Diana has some difficulty subduing Steve Trevor, presumably a slightly-above average human strength-wise, yet later she shows she can effortlessly lift a desk with one and and battle a Greek god.