How did the Jews win the war that started Hanukkah?

The spiritual answer is that they had God on their side, but the fact is that they were poorly equipped but had better battle tactics than the Syrian-Greeks.

Answer:"Better battle tactics" isn't enough to explain away the open miracle of the Maccabees' victories. Yes, "victories" plural. The battles were fought over a twenty-eight year period. In several occasions, the Maccabees faced Seleucid armies over ten times their size; and the Seleucids were equipped with elephants and were battle-hardened soldiers, whereas the Maccabees had not had any previous military training or experience. God's help is actually the only sound explanation, like it or not.