If Japan attacks UK, Anzac, or Us units when not at war she will have to fight all three. If Japan is already at war with UK/Anzac then she can choose to ignore the US units if not already at war with them.
The state of war commences at the beginning of the combat move so Japan will have to engage the war ship first.
Moving the Battleship can help some but if Japan is really determined to get the UK and Anzac ships she will. It should be possible to combine them all with the US fleet by turn 2 though (move from West Us-Pearl turn 1 and then Pearl to Queensland turn 2. So much depends on what Japan choose to do though. It is a little overwhelming at times.
It is especially overwhelming when public enemy number one is not an opposing player but a three year old convinced he is Loki. :P.