Tree-of-Heaven, aka Ailanthus, aka “That No Good Rotten Son of a Bitch” is in my experience the single most difficult invasive species to control for. It’s exceptionally stubborn and seems to resist every single control method that exists. It’s especially good at coming back from roots left in the ground, which can make it nearly impossible to completely kill.
Hand pulling can work, but unless you get all of the roots it’s just going to keep growing. If you don’t get all of the roots and a network starts growing under the ground, it will just keep coming back. If there is an adult tree somewhere nearby, you have to kill that.
I have seen some success with chemical control. Both glyphosate and triclopyr seem to be effective on it (legal disclaimer: consult the product labels and a locally licensed applicator before applying chemical control). I’ve successfully used foliar applications, hack-and-squirt, and cut-stump applications. However, even in these cases, it’s not uncommon to see parts of the tree hanging on or the roots sending a bunch of shoots up in response. It requires follow-up treatments to get full control over it.
Also, you aren’t going crazy about the smell. Personally, I’m pretty much nose blind so I can barely detect it but according to coworkers who have functioning noses it reeks. Last summer my crew had a lengthy discussion as to how to describe how it smells. The end conclusion was “a KFC sandwich that had been slathered with peanut butter and then left in the truck for a week”. Some of my coworkers use recognizing the smell as a key identification feature when they aren’t sure if they are looking at Ailanthus or not.
Aside from the smell, it’s not difficult to identify the plant from the leaves. They will be compound leaves (several leaflets on a single stalk forms one leaf). The image above shows a single leaf. Each leaflet will have smooth edges but near the base, there will be two small lobes. These lobes have a small gland on them. I’m unaware of any other trees that have leaves that look like that. Make sure to not confuse them with Ash, Walnut, Hickory, or Sumac which are all native trees in the Eastern United States that also have compound leaves. Their leaves will be a distinctly different shape.
Young leaves will have a distinct red color to them as they emerge. Like many young leaves, they might not perfectly resemble the shape of the fully grown leaves but the basic pattern will be visible. I have spoken with several people who use this red color as a key identifying feature.
The bark is typically smooth, but I have seen some cases where it gets highly textured. I recommend avoiding using that as a key feature.
Based on this Reddit thread.