You can test the straw for long-residual herbicide residues by creating a potting mix that is 1/3 ground straw and 2/3 lightweight, soilless growing media. Fill four pots with the mixture and two pots with just the potting soil by itself. Plant bean or pea seeds in all pots, and observe seed germination and plant growth for symptoms of curling, cupping, twisting, distortion, or stunting. This test is based on protocols like those linked below for contaminant screening, if you'd like to learn more:

• Conducting a Bioassay For Herbicide Residues -- NC State Extension
• Bioassay Test for Herbicide Residues in Compost -- Washington State University

There isn't really a useful lab test since the environmental testing lab (different from a standard soil testing lab) would need to know which exact herbicides to screen for.

Miri