Removed by OP

Could it be some type of Jasmine?

All of the jasmines I know have flat flowers, not tubular ones. Many people grow Confederate Jasmine around here and those are the ones I'm used to seeing. If there's a tubular blooming one, I don't know about it!

Melanie, it reminds me of my honeysuckle

The blooming shrub sucker is a Cestrum, likely Cestrum nocturnum. At the moment, I'm not sure what the vine is that is growing on it.

Night Blooming Jasmine (Cestrum nocturnum)

Danita nailed it! Jessamine, why didn't I think of that? Duh. Oh, and that vine that's growing on it is growing on everything I own. It's the highly invasive skunk vine (Paederia foetida). I will never be rid of it.

I'm trying to tell Dad what it was because I was showing him the pictures. I said it was Jessamine and he said, "In West Virginia, we call that jasmine." And then I had to explain how they're different things. This is why I hang out on ATP. Talking to non-gardeners can lead to frustration.

I have smelled it at night so one of my neighbors must have it. I wonder if a bird or other critter brought a seed to my yard. FYI, it happens to be growing right next to the pokeweed which also mysteriously appeared a few weeks ago. That area is just a hotbed for volunteers!

Mmmm, skunk vine... that sounds delightful.

Plants in the Jasminum genus would be true Jasmines.
As a common name, however, Jasmine and Jessamine do seem to be used fairly interchangeably for a wide variety of scented plants. The preference for using one or the other seems to be a regional thing.

That's why I like scientific names!