Would a ship or other vehicle be a valid target for teleport and plane shift spells if animated by Animated Objects or Aether Puppet?
Also would the maximum load for cargo be calculated by strength or left to the capacity of the original object?
Always their maximum load calculated by Strength, if it's a construct. An animated object(despite also being a spell effect via the spell) is still a Construct with distinct abilities granted at its creation regardless of its old function or form as an object. Considering you're likely dealing with a Colossal animated object for a ship, that usually isn't a problem, but you'd probably have difficulty targeting it with Teleport. Plane shift works fine. For other vehicles, just make sure they have the strength to support anything they're carrying- and that they're not carrying creatures beyond the spell's capacity.
Some spells also target a ship differently, due to it being more a collection of objects, but I can't seem to find that quote at the moment...