Look Up! Stay Alive!
(Caveat to this advice - it's from the Original Rulebook. If you are playing the new game then the rules may have changed, but look in the below section just in case.)
My question has to do with the invaders moving in and through the resource territories. Do the invaders need to declare a battle on the terr. and then capture it before moving through it?
See Action 2: Declare Battles on page 10 of the Rule Book.
"The player must declare which territories he plans to attack (if any) on the combat part of his turn. He does this by placing a battle marker in that territory and declaring that it is a "declared territory"."
It doesn't matter if it's the resource territory or not.