Thanks for editing your post to let us know what you learned.* I know of Saltcedar and he's good at id.* Hope you gave him a bit 'thanks'.* :)* I agree they are all trash trees, with the possible exception of the elm.
To id your elm you might want to post a picture of it at the UBC Botanical Gardens forum where several botanists hang out.* They are quite good at that type of id.* Here's their main forums page and the second link is where you should post it.* Do add your location in your profile so they won't have to ask and let them know where the tree grows.
I'd love to know what you find out.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.