Straw and Dirt stockpiles should be at least 300 large.
Unlike most other stockpiles straw and dirt take up 9 tiles. The tile they are on and all other adjacent tiles. So, a normal stockpile that only takes up one square holds 30+ of an object. Assuming straw and dirt would be around 35 (I would actually assume 50 or more) then 9 tiles worth of space would be 315 large.
Also, turning straw into bales should allow you to store it more efficiently in some way.