The basic mechanism is along with decomposing of straw, the phenolic compounds ex. lignin and other oxidized phenolics are leached slowly into the surrounding water. Indeed, lignin is persistent in nature. However, under aerobic condition, with the help of different bacterial and fungal enzyme activities lignin oxidized into fulvic and humic acids. The produced humic substances often termed as Dissolved Organic Carbon (DOC). When sunlight falls onto water containing humic substances, in the presence of dissolved oxygen (DO), hydrogen peroxide is formed. In fact, hydrogen peroxide can be formed on a regular basis under ample sunlight, as DOC production continues. The produced hydrogen peroxide is considered the main substance in controlling algae.
I would like to suggest you to do a laboratory test first. Using different parts of rice straw. Then you will be able to determine what part would be more effective. You can use, tanks with algae, and then add the parts in different weights. You may use Chlorophyll-a level as the measure, beginning and after.