Hey, drygulch, if this is the same tree, I share your revulsion. It is a horrible tree. Pops up everywhere from underground roots and if left unchecked will form its own forest. Not only does it stink, the sap can cause a serious skin rash. I hate this tree although I have one at the very western edge of my yard that I allow to stay for the shade it gives in summer. Right now, it's a PITA for sure and all the leaves - and branches - are dropping all over. Why anyone would plant this tree on purpose is a mystery to me.

Here is a link that might be useful: ailanthus altissima

Nope, not that one. It smells much like citrinellum, which also makes me ill. I'll try to find a link.

The tree that comes to mind for me, especially at this time of year, is the carob tree (Ceratonia siliqua). The downside is that it looks nothing like a eucalyptus. It is especially pungent on cold evenings and mornings and during dry spells. Ours did not produce much scent at all last year when it was so wet. This year it is quite pungent. A mature carob tree will 'scent' the entire neighborhood!

DH and I strongly disliked this odor our first year in this house (2003). This year we kinda like it. Weird.

Cheers~
Mary

Here is a link that might be useful: Carob Leaves

Nope. That's not it, either, and I'm having no luck finding it on the "net".

It may be that more than one plant exudes this particular odor...?

I used to have a eucalyptpus (microtheca I think) that drove me crazy when it bloomed - I couldn't stand the smell. It had gray-green leaves and cream-colored flowers.

A tree that may meet your description is the Willow Acacia (Acacia salicina). It has cream puffball flowers and is prone to suckering from roots that are close to the soil surface. It blooms heavily in the fall and its flowers attract butterflies, especially the Painted Lady. But, the blossoms do have a distinct odor and some folks object to it. The Australian acacias also have stinky roots. If you dig in the root zone of one it almost smells 'skunky'.