Studies on barley straw have been inconclusive. Google and look at the various university studies on the subject.
What most people can agree on is:
Barley straw is not effective on existing algae, only in preventing new algaeIt is only effective on certain kinds of filamentous algae. No specific chemical or mechanism has been identified for this abilityThe straw must be fully dried, and not hay, or it will add nutrients to the water and worsen the algae problemThe straw will still break down in the presence of nitrogen products, adding net nutrients to the water and encouraging plant and algae growth if it is not eventually removedOther than the long range addition of breakdown nutrients, it is not likely to be harmful to your pond, so is a safe experiment to try