On a hot dry sunny day, spray the weeds with the strongest vinegar you can find.

For seedling weeds, 10% (pickling) vinegar should work.

You didn't put down a cardboard weedblock first, did you?

More than likely what you are seeing is seeds from the straw you put down growing. Is that growth straight up green grass like? If so it is just what your straw was and it is not a real problem.
Humus is residual organic matter in soil. Hummus is something people eat.

Straw should not have much in the way of seeds since it's the stalks of wheat or other grains, leftover after the grain is removed. Hay, on the other hand, is a mixture of grasses with lots of seeds included.

If the vinegar doesn't work, you could add more mulch, or you could break down and use some defoliant like glyphosate, if you're not planning to plant other things immediately.

The issue I'm seeing is that if the weeds are growing now, what will stop them from growing after the yard is replanted?

Thanks to all of you! In response:
- yes, we did put down cardboard/newspaper first, then put the compost, straw & humus on top of it.
- yes, it's straight up like grass. and thanks for the correction re: humus v. hummus! Love 'em both.
- will try the vinegar, glyphosate, or just get the dh out there to pull out the seedlings w/me.
- yes, mad gallica, I guess we'll be spending a bit of time out there pulling them up as they germinate. We've put in stepping stones, rocks & drought resistance plants in place of the lawn & will just have to keep an eye on the seedlings. At least we can see the seedlings as they pop up through the bark.
Thanks again to all of you to helping me out.

When grains, wheat, oats, rye, etc., are harvested some seeds cling to the stalks. I have only seen seed free straw in the very expensive bales that have been processed, the seed heads removed, and packaged on plastic. If those seeds do grow after the grass is seeded a mowing or two will be all that is needed to control it.

Its unusual to see weeds coming up the way you described when cardboard is there as an underlayment. If they're just rooted in the mulch on top, they ought to be easy to pull.

What will keep them from coming up later is established sod. Some will still probably come up and it may compete with a seeded lawn (which is a better option IMO).

Which is why it is a good idea to follow up sheet composting with soil sterilization. Till everything in and lay a thick clear plastic (weight it down so it won't blow away). It'll probably take about a month or two of high temps and lots of sun but it'll kill weed seeds down to 18" depending on how long you leave it on and how much sun it gets. You have to wet it down thoroughly before laying the plastic.

It will not kill worms, they will just move out of the area until it cools down again. It takes time for the soil to heat up and that gives soil fauna plenty of time to vacate the premises.

Yes, more time spent before you can see the results - but much less time spent down the road a ways.