Utena is probably my favourite anime of all time but am I missing something or do the duels lack any strategy whatsoever? Whenever Utena starts to lose she (almost always) uses that attack where the prince descends to one-hit KO her opponent.
Yep, the duels lack all strategy, and that's by design. The duels are never really supposed to be demonstrations of physical strength - they're articulations of resolve, continuations of the emotional arguments each relevant character has been proposing through that arc. Characters are fighting to uphold their conviction in something, and Utena keeps winning because her conviction keeps proving itself stronger - her childish faith and obliviousness to the complexities of everyone else's situations is actually what makes her strong, whereas everyone else is fighting for things they can't say they're entirely certain of. That's why Utena only loses when she doubts her identity, and why the car speech always starts with "if your soul has not yet given up" - it's the characters maintaining some sort of core conviction that gives them the strength to fight.