Here are the pics, not sure why they are not showing up...

Where do you live?
What kind of grass do you have/want?

Believe it or not, the answers are pertinent to what your weeds are. Some weeds from one part of the world look like different weeds in another part of the world. And can you take the pictures again in the shade. The contrast is too high to clearly see which is weed and which is grass.

Ok, here are some new pics. Not sure what to do about this mess...

Any ideas?

Just spray the weeds with weed killer. Weed B Gone max and Weed B Gone Clover, chickweed and oxalis killer with either a tank sprayer or a hose end sprayer. Read all labels and follow them.

Tried it, 5 days in a row. nothing.

Mow real low.

Buy a hose end sprayer and concentrate.

Put a couple drops of dish soap in the bottle and spray away.

I took the different weeds to a nursery and they told me, and they weren't certain about it - but they thought it might be

Chick weed
Some type of Cilantro
Loose Strife

He wasn't sure, but that is what he thought.

So you sprayed weed killer 5 days in a row????? Certainly not a recommended practice. What did you use? Weed killer takes a while to start working. It usually takes 2 weeks for death, but you should see weeds curling and discoloring after a week. Weed killers are most effective when weeds are actively growing, so they take longer with cooler temps, and during periods of no rain.