First shrub is a privet, second probably a viburnum. After that there's a birch...

Yes, the first one is chinese privet, a category 1 invasive plant in much of the southeast. Destroy those berries! Cut it down, paint the stump with brush-b-gone.

The second one does resemble a Viburnum, perhaps V. dentatum or it's cousin Viburnum recognitum.

The third one might be musclewood, Carpinus caroliniana (American hornbeam is the other name).

The fourth one looks like it could be a member of the Carya genus (which include pecan,hickory and others). What does the terminal bud look like?

Then a bunch of stuff I don't know ...

Then the last one looks like a Geum.

Yes: A Carpinus rather than a birch.

The last one looks like my Geum canadense. I believe you do have Berchemia scandens (a vining plant)...the other one you mentioned is a tree and has smaller berries. And the thorny plant which was the last woody plant might be Gum Bumelia (Sideroxylon lanuginosum).

Thanks guys. Any guess on the Ligustrum species? I couldn't reach any of the hickory shoots. Somehow I missed that Berchemia scandens was a vine but it makes sense now.

That is Ligustrum sinense, chinese privet.

Ligustrum sinense is deciduous, with leaves "elliptic to oblong, 1-3 in. long, acute or obtusish, tapering at base" (Bailey, 1949). I'm inclined to think this is another species.

Ligustrum sinense is NOT deciduous in Georgia and I imagine that is true in Texas as well. It is all I see on roadsides now that the leaves have fallen off other plants.

I'm sure the size and shape of the leaves vary a bit; the ones shown by the original post look exactly like chinese privet in my area.

Here is a link that might be useful: picture