Nothing is immune to poison unless it specifically says in their special rules. That is usually only in named characters or by magic items from the army list.
The confusion comes because the BRB says 'unliving' things (or something like) aren't effected by poison. In this case, it doesn't refer to undead it refers to wood and metal like warmachines, chariots and steam tanks. Undead are effected by poison.
Actually chariots are affected by poison, on page 96 of the BRB it says because a chariot includes elements that is vurnarable to poison (steeds, riders) chariots are not immune. Had to check that up as I have been taking out a ton of chariots with my skinks and was afraid i had been "cheating" in several tournament games ^^. I know that they were immune in 6th ed tho. War machines are immune (cant imagine how a poison dart would damage a steam tonk or a cannon) as you say, but keep in mind that the crew is not, so any poison hit randomized to hit the crew doesnt need to roll to wound.
Also, the Dwarf Gyrocopter is considered a war machine in some respects, but not when it comes to poison: it's susceptible, as per the Dwarf FAQ.